Imaging processing method for mapping video source information onto a displayed object

ABSTRACT

An image processing apparatus and the method for mapping a plurality of images which are on the two-dimensional plane on the corresponding faces of a solid in the three-dimensional virtual space. The mapping image on the side face being close to the object image displaying face is formed in accordance with the shape of object image displaying face of the solid on which the object image is mapped, and the image mapped on each face is displaced in accordance with the movement of the solid in the three-dimensional space. Therefore, the image that as if a desired image is stuck to the faces of the solid moving in a virtual space can be displayed on a screen surface by easily operating by an operator.

TECHNICAL FIELD

The present invention relates to an image processing apparatus and animage processing method, and is applicable to the case where an imageprojected on a two-dimensional plane is displayed on a face of a solidformed in a three-dimensional space.

BACKGROUND ART

Conventionally, there has been provided a special effect device (DVE:Digital Video Effects) which gives video signal the special effects suchas, cropping of image (Crop), skewing (Skew), and variation in theX-axis direction and the Y-axis direction (XY-rate) to transform animage. It has been considered that the device is used to obtain "Slab"effect for displaying an image on a face of a rectangular parallelepipedformed in a three-dimensional space.

More specifically, as shown in FIG. 1, in the "Slab" effect processing,a moving picture displayed on a two-dimensional plane is referred to asan object image (Object), and the special effect device is used to forman image that the object image seems to be stuck to an object imagedisplaying face (SideA) of a rectangular parallelepiped formed in athree-dimensional space.

In the "Slab" effect, as well as the face on which the object image isdisplayed (SideA), two side faces (SideB and SideC) are simultaneouslydisplayed in accordance with an inclination of the rectangularparallelepiped in a three-dimensional space. FIG. 2 shows a method offorming the three-dimensional six-side display image by using onespecial effect device (DVE).

That is, in FIG. 2, a first video tape recorder (VTR) 6 is used toreproduce an object image (Object) which is output to a special effectdevice 5. The special effect device 5 performs the mapping processing inwhich the reproduced object image (Object) seems to be stuck to theobject image displaying face (SideA) of the three-dimensional six-sidedisplay image, which is output to a second video tape recorder (VTR) 7.The second video tape recorder 7 records the object image displayingface (SideA) being the object image (Object).

An operator reproduces by a third video tape recorder 8 a video tape inwhich the object image displaying face (SideA) is thus recorded, andoutputs it to a composing circuit 9. At this time, the operator alsoreproduces, on a two-dimensional plane by the first video tape recorder6, an image to be displayed on the side face (SideB) of thethree-dimensional six-side display image. The image reproduced by thefirst video tape recorder 6 is output to the special effect device 5 andthe special effect processing is performed on it.

Thus, the image on a two-dimensional plane reproduced by the first videotape recorder 6 is transformed into the shape which seems to bedisplayed on the side face (SideB) of the three-dimensional six-sidedisplay image. The image of side face (SideB) is composed with theobject image displaying face (SideA) at the composing circuit 9. At thistime, the operator uses a specified operation key to adjust the displayposition so that the object image displaying face (SideA) and the sideface (SideB) are close at one edge each other. The composed image of theobject image displaying face (SideA) and the side face (SideB) obtainedat the composing circuit 9 is recorded at the second video tape recorder7.

The operator reproduces at the third video tape recorder 8 the videotape in which the composed image of the object image displaying face(SideA) and the side face (SideB) is recorded, and outputs it to thecomposing circuit 9. At this time, the operator also reproduces theimage to be displayed on the side face (SideC) of the three-dimensionalsix-side display image on a two-dimensional plane by the first videotape recorder 6. The image reproduced by the first video tape recorder 6is output to the special effect device 5 and the special effectprocessing is performed on it.

Thus, the image on a two-dimensional plane reproduced by the first videotape recorder 6 is transformed into the shape which seems to bedisplayed on the side face (SideC) of the three-dimensional six-sidedisplay image. The image of side face (SideC) is composed with thecomposed image of the object image displaying face (SideA) and the sideface (SideB) at the composing circuit 9. At this time, the operator usesa specified operation key to adjust the display position so that theobject image displaying face (SideA) and the side face (SideB), and theobject image displaying face (SideA) and the side face (SideC) arerespectively close at one edge each other.

The three-dimensional six-side display image obtained at the composingcircuit 9 is recorded at the second video tape recorder 7.

By the way, in the case of forming the three-dimensional six-sidedisplay image by using the above method, the side faces (SideE andSideC) are formed separately from the object image displaying face(SideA) for displaying an object image (Object) and are composed.Accordingly, when the inclination of three-dimensional six-side displayimage is changed in a three-dimensional space, even if the specialeffects such as, cropping of image (Crop), skewing (Skew), and variationin the X-axis direction and the Y-axis direction (XY-rate), on theobject image displaying face (SideA) are changed, the side faces (SideBand SideC) are not followed. Therefore, it is also needed to change thespecial effects to the side faces (SideB and SideC) in accordance withthe change of the object image displaying face (SideA) in thethree-dimensional space.

In this case, an operator has to perform the work of composing the sidefaces (SideB and SideC) manually for each frame (60 frames per second)in accordance with the change of the object image displaying face(SideA). There has been a problem that the operation of operator becomescomplicated.

DISCLOSURE OF INVENTION

The object of this invention is to solve the above problem and toprovide an image processing method which can improve the operationalefficiency when the transformation of each plane of three-dimensionalthree-side display image are simultaneously executed to connect eachplane with one another and the special effects are given.

To solve the above problem, this invention provides: a first imageforming means for forming an object image by writing a first image in afirst memory and transforming said first image written in said firstmemory based on a first control data input from a predetermined controlmeans; a second image forming means for forming a first side image bywriting a second image in a second memory and transforming said secondimage written in said second memory into the image having a shapecorresponding to said object image based on a second control data inputfrom said control means; a third image forming means for forming asecond side image by writing a third image in a third memory andtransforming said third image written in said third memory into theimage having a shape corresponding to said object image based on a thirdcontrol data input from said control means; and a control means formoving said object image, said first side image, and said second sideimage in accordance with the movement of said solid having predeterminedfaces respectively corresponding to said object image, said first sideimage, and said second side image in the three-dimensional space, andfor perspective-transforming on a predetermined screen surface saidobject image, said first side image, and said second side image mappedon said solid.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a schematic diagram explaining a three-dimensional three-sidedisplay image;

FIG. 2 is a schematic diagram explaining a conventional method offorming a three-dimensional image;

FIG. 3 is a block diagram showing the entire construction of an imageprocessing apparatus according to the present invention;

FIG. 4 is a schematic diagram explaining the definition of screensurface;

FIG. 5 is a schematic diagram explaining the basic three-dimensionalmoving transformation and perspective transformation;

FIG. 6 is a schematic diagram explaining the basic three-dimensionalmoving transformation and perspective transformation;

FIGS. 7A and 7B are schematic diagrams explaining the basicthree-dimensional moving transformation and perspective transformation;

FIG. 8 is a schematic diagram explaining a solid (a rectangularparallelepiped) being at the basic position in the three-dimensionalspace;

FIGS. 9A and 9B are schematic diagrams explaining the source videosignal of an object image;

FIGS. 10A and 10B are schematic diagrams explaining the transformationof the object image in the z-axis direction;

FIGS. 11A and 11B are schematic diagrams explaining the change of theobject image;

FIGS. 12A and 12B are schematic diagrams explaining the source videosignal of a first side face image;

FIGS. 13A and 13B are schematic diagrams explaining the parallelmovement of the source video signal of the first side face image;

FIGS. 14A and 14B are schematic diagrams explaining the transformationof the source video signal of the first side face image;

FIG. 15A is a schematic diagram explaining the cropping priority mode;

FIG. 15B is a schematic diagram explaining the reduction/magnificationrate priority mode;

FIGS. 16A and 16B are schematic diagrams explaining the rotatingtransformation around the x-axis of the source video signal of the firstside face image;

FIGS. 17A and 17B are schematic diagrams explaining the case where thesource video signal of the first side face image is inclined by an angleθ_(B) for the x-axis;

FIGS. 18A and 18B are schematic diagrams explaining the movement foroverlapping the source video signal of a first side face image on thefirst side face of the solid;

FIGS. 19A and 19B are schematic diagrams explaining the source videosignal of a second side face image;

FIGS. 20A and 20B are schematic diagrams explaining the parallelmovement of the source video signal of the second side face image;

FIGS. 21A and 21B are schematic diagrams explaining the transformationof the source video signal of the second side face image;

FIG. 22A is a schematic diagram explaining the cropping priority mode;

FIG. 22B is a schematic diagram explaining the reduction/magnificationrate priority mode;

FIGS. 23A and 23B are schematic diagrams explaining the rotatingtransformation around the x-axis of the source video signal of thesecond side face image;

FIGS. 24A and 24B are schematic diagrams explaining the case where thesource video signal of the second side face image is inclined by anangle θ_(c) for the x-axis;

FIGS. 25A and 25B are schematic diagrams explaining the movement foroverlapping the source video signal of a second side face image on thesecond side face of the solid;

FIG. 26 is a flowchart showing the procedure of mapping the first sourcevideo signal;

FIG. 27 is a schematic diagram explaining the case where the firstsource video signal is mapped on the object image displaying face of thesolid;

FIG. 28 is a schematic diagram explaining the time when the first sourcevideo signal is mapped on the plane facing the object image displayingface of the solid;

FIG. 29 is a flowchart showing the procedure of mapping the secondsource video signal;

FIG. 30 is a schematic diagram explaining the case where the secondsource video signal is mapped on the first side face of the solid;

FIG. 31 is a schematic diagram explaining the case where the secondsource video signal is mapped on the plane facing the first side face ofthe solid;

FIG. 32 is a flowchart showing the procedure of mapping the third sourcevideo signal;

FIGS. 33A and 33B are schematic diagrams explaining the inversionprocessing of the image mapped on the face of solid in the horizontaldirection;

FIGS. 34A and 34B are schematic diagrams explaining the inversionprocessing of the image mapped on the face of solid in the verticaldirection; and

FIG. 35 is a schematic diagram explaining the inversion processing ofthe image mapped on the face of solid.

BEST MODE FOR CARRYING OUT THE INVENTION

(1) Entire Construction

FIG. 3 generally shows an image processing apparatus 10 using a specialeffect device. An operator operates a control panel 56 to input thecommand signal to an CPU 58 via an interface circuit (I/F) 57 and a busBUS. The CPU 58 uses an ROM (Read Only Memory) 59 and an RAM (RandomAccess Memory) 61 to respectively control an image forming part 20 ofthe object image displaying face (SideA) of the three-dimensionalsix-side display image, the image forming part 30 of the first side face(SideB), and the image forming part 30 of the second side face (SideC)by the command from the operator.

The image forming part 20 of the object image displaying face (SideA)inputs the source video signal V_(1A) of the object image (Object)before transformation to a cropping circuit 21. The cropping circuit 21crops the source video signal V_(A) at the cropping position (C_(AL),C_(AR), C_(AT), C_(AB)) of the X-Y coordinates which is input from theCPU 58 via the bus BUS, and stores it in a frame memory FM₂₂ with theform that it is not transformed.

Here, a read address generating circuit 25 generates a read address(X_(MA), Y_(MA)) from the frame memory FM₂₂, based on the data of theaddress (X_(S), Y_(S)) on a monitor screen 55 output from a screenaddress generating circuit 51 and the data of the parameters b_(A11) tob_(A33) of the image transformation matrix specified by the CPU 58.

The frame memory FM₂₂ reads the stored video signal by the read address(X_(MA), Y_(MA)) output from the read address generating circuit 25. Asa result, the cropped source video signal V_(1A) in the frame memoryFM₂₂ is image-transformed so that the cropped portion of the sourcevideo signal V_(1A) is mapped on the object image displaying face(SideA) of the three-dimensional six-side display image actuallydisplayed on the monitor screen 55 among solids (rectangularparallelepipeds) in the virtual three-dimensional space. The transformedvideo signal V_(3A) thus obtained is output to a mixer 53.

Further, in the image forming part 20 of the object image displayingface (SideA), similar to the case of the source video signal V_(1A), keysignal K_(1A) is cropped by a cropping circuit 23, thereafter, it isstored in a frame memory FM₂₄ as it is. The frame memory FM₂₄ reads thevideo signal by the read address (X_(MA), Y_(MA)) output from the readaddress generating circuit 25, so as to obtain the transformed keysignal K_(3A) transformed similar to the case of the transformed videosignal V_(3A) described above, and it is output to the mixer 53 togetherwith the transformed video signal V_(3A).

In connection, the key signal is that the image plane formed by thesource video signal V_(1A) described above is constructed by datasequence of "0" or "1". When the source video signal V_(1A) is croppedor image-transformed, only data at the portion that the processing isapplied is changed.

On the contrary, the image forming part 30 of the first side face(SideB) inputs the source video signal V_(1B) before transformation ofthe picture displayed on the first side face (SideB) of thethree-dimensional six-side display image to a cropping circuit 31. Thecropping circuit 31 crops the source video signal V_(1B) at the croppingposition (C_(BL), C_(BR), C_(BT), C_(BB)) of the X-Y coordinates whichis input from the CPU 58 via the bus BUS, and stores it in a framememory FM₃₂ with the form that it is not transformed.

Here, a read address generating circuit 35 generates a read address(X_(MB), Y_(MB)) from the frame memory EM₃₂, based on the data of theaddress (X_(S), Y_(S)) on the monitor screen 55 output from the screenaddress generating circuit 51 and the data of the parameters b_(B11) tob_(B33) of the image transformation matrix specified by the CPU 58.

The frame memory FM₃₂ reads the stored video signal by the read address(X_(MB), Y_(MB)) output from the read address generating circuit 35. Asa result, the cropped source video signal V_(1B) in the frame memoryFM₃₂ is image-transformed so that the cropped portion of the sourcevideo signal V_(B) is mapped on the first side face (SideB) of thethree-dimensional six-side display image actually displayed on themonitor screen among solids (rectangular parallelepipeds) in the virtualthree-dimensional space. The transformed video signal V_(3B) thusobtained is output to a mixer 52.

Further, in the image forming part 30 of the first side face (SideB),similar to the case of the source video signal V_(1B), key signal K_(1B)is cropped by a cropping circuit 33, thereafter, it is stored in a framememory FM₃₄ as it is. The frame memory FM₃₄ reads the video signal bythe read address (X_(MB), Y_(MB)) output from the read addressgenerating circuit 35, so as to obtain the transformed key signal K_(3B)transformed similar to the case of the transformed video signal V_(3B)described above, and it is output to the mixer 52 together with thetransformed video signal V_(3B).

On the contrary, the image forming part 40 of the second side face(SideC) inputs the source video signal V_(1C) before transformation ofthe picture displayed on the second side face (SideC) of thethree-dimensional six-side display image to a cropping circuit 41. Thecropping circuit 41 crops the source video signal V_(1C) at the croppingposition (C_(CL), C_(CR), C_(CT), C_(CB)) of the X-Y coordinates whichis input from the CPU 58 via the bus BUS, and stores it in a framememory 42 with the form that it is not transformed.

Here, a read address generating circuit 45 generates a read address(X_(MC), Y_(MC)) at the frame memory FM₄₂, based on the data of theaddress (X_(S), Y_(S)) on the monitor screen 55 output from the screenaddress generating circuit 51 and the data of the parameters b_(C11) tob_(C33) of the image transformation matrix specified by the CPU 58.

The frame memory FM₄₂ reads the stored video signal by the read address(X_(MC), Y_(MC)) output from the read address generating circuit 45. Asa result, the cropped source video signal V_(1C) in the frame memoryFM₄₂ is image-transformed so that the cropped portion of the sourcevideo signal V_(1C) is mapped on the second side face (SideC) of thethree-dimensional six-side display image actually displayed on themonitor screen among solids (rectangular parallelepipeds) in the virtualthree-dimensional space. The transformed video signal V_(3C) thusobtained is output to the mixer 52.

Further, in the image forming part 40 of the second side face (SideC),similar to the case of the source video signal V_(1C), key signal K_(1C)is cropped by a cropping circuit 43, thereafter, it is stored in a framememory FM₄₄ as it is. The frame memory FM₄₄ reads the video signal bythe read address (X_(MC), Y_(MC)) output from the read addressgenerating circuit 45, so as to obtain the transformed key signal K_(3C)transformed similar to the case of the transformed video signal V_(3C)described above, and it is output to the mixer 53 together with thetransformed video signal V_(3C).

The mixer 52 composes the transformed video signal V_(3B) output fromthe image forming part 30 of the first side face (SideB) and thetransformed video signal V_(3C) output from the image forming part 40 ofthe second side face (SideC), and at the same time, composes thetransformed key signal K_(3B) output from the image forming part 30 ofthe first side face (SideB) and the transformed key signal K_(3C) outputfrom the image forming part 40 of the second side face (SideC). Thereby,the composed video signal V_(BC) and the composed key signal K_(BC) areobtained, which are composed so that the first side face (SideB) and thesecond side face (SideC) are close each other. The composed video signalV_(BC) and the composed key signal K_(BC) are output to the mixer 53.

The mixer 53 composes the transformed video signal V_(3A) output fromthe image forming part 20 of the object image displaying face (SideA)and the composed video signal V_(BC) output from the mixer 52, and atthe same time, composes the transformed key signal K_(3A) output fromthe image forming part 20 of the object image displaying face (SideA)and the composed key signal K_(BC) output from the mixer 52. Thereby,the composed video signal V_(ABC) and the composed key signal K_(ABC)can be obtained. The composed video signal V_(ABC) and the composed keysignal K_(ABC) represent the three-dimensional six-side display imagethat the object image displaying face (SideA), the first side face(SideB), and the second side face (SideC) are close with one another.

The composed video signal Van and the composed key signal K_(ABC) outputfrom the mixer 53 are output to an output processor 54. The outputprocessor 54 adds the cubic effect given by shadowing a picture (dropshadowing effect) or the effect of making a moving picture to trail(trailing effect), and outputs the obtained output video signal V_(OUT)to the monitor screen 55 to display the picture.

(2) Definition of Coordinates

The three-dimensional coordinates used in this embodiment for generatinga three-dimensional six-side display image and for displaying it on themonitor screen 55 is defined by the orthogonal coordinates of x-axis,y-axis, and z-axis. More specifically, as shown in FIG. 4, assuming thatthe screen surface 55A exists on the xy-plane defined by the x-axis andy-axis which is orthogonal to the x-axis, the x-axis is defined as thehorizontal (right and left) direction of the screen surface 55A, and they-axis is defined as the vertical (up and down) direction of the screensurface 55A.

Further, the depth direction of the screen surface 55A is defined as theplus direction of the z-axis which is orthogonal to the xy-plane, andthis side of the screen surface 55A, that is the side where view pointPZ for viewing the screen surface exists, is defined as the minusdirection of the z-axis.

Further, it is defined that the center of the screen surface 55Acoincides with the origin O of the three-dimensional coordinatescomposed of x-axis, y-axis, and z-axis.

The virtual coordinates values, which continue from the inside (origin)of the screen area toward the right and left outside direction, is seton the x-axis. The virtual coordinates values between "-4" and "4" areset from the left side to the right side when viewing the screen surface55A from the view point PZ on the x-axis in the screen area.

Further, the virtual coordinates values, which continue from the inside(origin) of the screen area toward the up and down outside direction,are set on the y-axis. The virtual coordinates values between "-3" and"3" are set from the down side to the up side when viewing the screensurface 55A from the view point PZ on the y-axis in the screen area.

Further, the view point position PZ of the operator is virtually set atthe position where the coordinates value becomes "-16" on the z-axis.

(3) Basic Algorism of Three-Dimensional Transformation

The basic algorism of three-dimensional image transformation processingwill be described, which is for fornling a solid (a rectangularparallelepiped) at an arbitrary position and with an arbitrary angle ina virtual space represented by three-dimensional coordinates of xyz, andfor displaying only the plane actually viewed from the view point ofoperator, which is positioned at the coordinate value "-16" of thez-axis, of the solid on the screen surface 55A as the three-dimensionalsix-side display image.

The source video signal forming the image of two-dimensional plane isstored in a frame memory in the state that it is not transformed.Therefore, as shown in FIGS. 5 and 6, the source video signal V₁ existson the xy-plane in a space represented by the three-dimensionalcoordinates of xyz, so that the image of the source video signal V₁ isdisplayed on the screen surface 55A which exists on the xy-plane.

In connection, FIG. 5 shows the state where the space represented by thethree-dimensional coordinates of xyz is viewed from the plus side of they-axis to the minus side, and the source video signal V₁ is overlappedon the screen surface 55A which exists on xy-plane. FIG. 6 shows thestate where the space represented by the three-dimensional coordinatesof xyz is viewed from the view point PZ on the z-axis to the minus sideof the z-axis through the screen surface 55A, and the source videosignal V₁ exists in the screen surface 55A on xy-plane.

The operator operates the operation key of the control panel so that thethree-dimensional image transformation processing is performed on thesource video signal V₁ in the xyz-coordinate space. More specifically,the three-dimensional transformation matrix T₀ composed of parametersset for each frame is performed for each pixel of the source videosignal V₁ by the operation of operator, so that the source video signalV₁ is three-dimensional-transformed in the spatial position indicated bythe three-dimensional transformed video signal V₂. The three-dimensionaltransformation in the case of FIGS. 5 and 6 is an example that thesource video signal V₁ is rotated by approximately 45° with the y-axisbeing centered, and moreover parallel moved in the plus direction of thez-axis.

The three-dimensional transformation matrix T₀ used forthree-dimensional transformation is represented by the followingequation: ##EQU1##

The parameters r₁₁ to r₃₃ used for the three-dimensional transformationmatrix T₀ include: a factor for rotating the source video signal V₁around the x-axis, around the y-axis, and around the z-axis; a factorfor magnifying/reducing a scale of the source video signal V₁ in thex-axis direction, y-axis direction, and z-axis direction respectively;and a factor for skewing the source video signal V₁ in the x-axisdirection, y-axis direction, and z-axis direction respectively. Theparameters "l_(x) ", "l_(y) ", and "l_(z) " include a factor forparallel moving the source video signal V₁ in the x-axis direction,y-axis direction, and z-axis direction respectively. The parameter "s"includes a factor for magnifying/reducing uniformly the entire sourcevideo signal V₁ in the respective direction of three dimensions.

Also, since the transformation matrix T₀ expresses the coordinates ofrotation transformation, etc. and the coordinates of parallel movementtransformation and magnification/reduction transformation in the samecoordinates, it becomes four lines and four rows. This matrix isgenerally called as the homogeneous coordinates.

When the source video signal V₁ on the screen surface 55A isthree-dimensional-transformed at the position of the three-dimensionaltransformed video signal V₂ by the three-dimensional transformationmatrix T₀, the three-dimensional transformed video signal V₂ isprojected onto the xy-plane by the perspective transformation matrix.

The perspective transformation is, as shown in FIGS. 5 and 6, atransformation for obtaining the image of the three-dimensionaltransformed video signal V₂ which is seen through on the xy-plane (thisis called as the perspective transformed video signal V₃) when thetransformed video signal V₂ is viewed from the virtual view point PZ onthe z-axis. In the case of FIG. 5, the perspective transformed videosignal V₃ is generated on the screen surface 55A of xy-plane by theperspective transformation matrix P₀, in which it seems as if there isthe image of the three-dimensional transformed video signal V₂ at theopposite side (the plus side of the z-axis) of the screen surface 55Aviewing from the virtual view point PZ.

The perspective transformation matrix P₀ is represented by the equation:##EQU2##

The parameter P_(Z) of the perspective transformation matrix P₀ is aperspective value for applying rules of perspective when thethree-dimensional transformed video signal V₂ is seen through onxy-plane. That is, in the case of FIG. 5, the three-dimensionaltransformed video signal V₂ in the three-dimensional space is inclinedfor xy-plane by 45°. The portion which is distant from the virtual pointPZ is seen small and the portion which is close to the virtual point PZis seen large, when the three-dimensional transformed video signal V₂ isseen from the virtual point PZ. Therefore, by using the parameter P_(Z),the perspective transformed video signal V₃ transformed to the positionof the screen surface 55A becomes that the three-dimensional transformedvideo signal V₂ in the three-dimensional space is transformed inaccordance with the distance from the virtual view point PZ.

The position where the three-dimensional transformed video signal V₂ istransformed on the screen surface 55A by the perspective transformationchanges in accordance with the distance between the virtual view pointPZ and the screen surface 55A, and the distance between the virtual viewpoint PZ and the three-dimensional transformed video signal V₂. Theperspective value P_(Z) is set by operator in accordance with theposition of the virtual view point PZ, so as to perform the perspectivetransformation in accordance with the position of virtual view point PZ.Usually, since the position of view point PZ is the coordinate value ofthe z-axis, "-16", the perspective value P_(Z) is so set that "1/16" isthe reference value.

In this way, the basic processing of three-dimensional transformationcomprises a spatial image transforming step for obtaining thethree-dimensional transformed video signal V₂ from the source videosignal V₁ by the three-dimensional transformation matrix T₀, and aperspective transforming step for transforming the three-dimensionaltransformed video signal V₂ obtained at the spatial image transformingstep by the perspective transformation matrix P₀. Therefore, thetransformation matrix T for obtaining the perspective transformed videosignal V₃ from the source video signal V₁ is represented by thefollowing equation as a multiplication equation of the three-dimensionaltransformation matrix T₀ and the perspective transformation matrix P₀ :##EQU3##

Here, in the image processing apparatus using the special effect deviceaccording to this invention, the two-dimensional source video signal V₁supplied from outside is written once in a frame memory FM and the readaddress two-dimensionally calculated is supplied to the frame memory FM,so that the spatial image transformation (three-dimensional imagetransformation and perspective image transformation) desired by anoperator can be performed on the video signal read from the frame memoryFM. Therefore, both of the source video signal V₁ stored in the framememory FM and the perspective transformed video signal V₃ read from theframe memory FM are two-dimensional data. In the calculation of readaddress, data in the z-axis direction on the three-dimensional space isnot used practically.

Therefore, the parameters of third line and third row for calculatingthe data in the z-axis direction in the equation (3) is not needed tocalculate the read address of the frame memory FM.

Thereby, assuming that the three-dimensional transformation matrixhaving the parameters necessary for calculation of the actualtwo-dimensional read address is "T₃₃ ", the matrix T₃₃ can berepresented by the following equation, omitting the parameters in thirdline and third row from the equation (3): ##EQU4##

Here, the relationship between the positional vector on the frame memoryFM and the positional vector on the monitor screen 55 will be describedbelow.

In FIG. 7A, the two-dimensional address on the frame memory FM is(X_(M), Y_(M)) and the positional vector is [X_(M) Y_(M) ]. In FIG. 7B,the address on the monitor screen 55 is (X_(S), Y_(S)) and thepositional vector is [X_(S) Y_(S) ]. When the two-dimensional positionalvector [X_(M), Y_(M) ] on the frame memory FM is expressed by thehomogenous coordinates, it can be expressed as vector [x_(m) y_(m) H₀ ].Also, when the positional vector [X_(S) Y_(S) ] on the monitor screen 55is expressed by the homogeneous coordinates, it can be expressed as avector [x_(s) y_(s) 1].

In addition, the parameter "H₀ " of the homogeneous coordinates is aparameter for representing the magnification/reduction rate of thevector.

In this way, the three-dimensional transformation matrix T₃₃ is effectedto the positional vector [x_(m) y_(m) H₀ ] on the frame memory FM, sothat the positional vector [x_(m) y_(m) H₀ ] on the frame memory FM istransformed into the positional vector [x_(s) y_(s) 1] on the monitorscreen 55. Therefore, the relation equation between the positionalvector [x_(m) y_(m) H₀ ] on the frame memory FM and the positionalvector [x_(s) y_(s) 1] on the monitor screen 55 is expressed by thefollowing equation:

    [x.sub.s y.sub.s 1]=[x.sub.m y.sub.m H.sub.0 ]·T.sub.33 (5)

In addition, the relationship between the parameter "H₀ " of thehomogeneous coordinates used in the positional vector [x_(m) y_(m) H₀ ]on the frame memory FM and the parameter "1" of the homogeneouscoordinates used in the positional vector [x_(s) y_(s) 1] on the monitorscreen 55 expresses that the positional vector [x_(m) y_(m) ] of thehomogeneous coordinates on the frame memory FM is transformed by thethree-dimensional transformation matrix T₃₃ into the positional vector[x_(s) y_(s) ], and that a value "H₀ " of the positional vector [x_(m)y_(m) ] of the homogeneous coordinates on the frame memory FM istransformed into a value "1" of the positional vector [x_(s) y_(s) ] ofthe homogeneous coordinates on the monitor screen 55.

In this way, the equation (5) is a relation equation for obtaining thepoint on the monitor screen 55 corresponding to the point on the framememory FM by the matrix T₃₃. Here, in the image processing apparatususing the special effect device, the source video signal is stored inthe frame memory FM with the state before transformation, and the pointof the frame memory FM corresponding to the point on the monitor screen55 obtained by the transformation matrix T₃₃ is specified by the readaddress, so that the spatial image transformation is performed on thesource video signal.

In this apparatus, it is not necessary to calculate by the equation (5)to obtain the point on the monitor screen 55 corresponding to the pointon the frame memory FM, but to obtain the point on the frame memory FMcorresponding to the point on the monitor screen 55. Therefore, theequation (5) is transformed to use the relation equation expressed bythe following equation:

    [x.sub.m y.sub.m H.sub.0 ]=[x.sub.s y.sub.s 1]·T.sub.33.sup.-1 (6)

so that when the positional vector [x_(s) y_(s) 1] on the monitor screen55 is specified, the positional vector [x_(m) y_(m) H₀ ] on the framememory FM is calculated by the transformation matrix T₃₃ ⁻¹. Thetransformation matrix T₃₃ ⁻¹ is the inverse matrix of the transformationmatrix T₃₃.

Next, to obtain the two-dimensional positional vector [X_(M) Y_(M) ] onthe frame memory FM, the transformation matrix T₃₃ and the inversematrix T₃₃ ⁻¹ are set as described below. More specifically, respectivefactors of the transformation matrix T₃₃ are set to parameters a₁₁ toa₃₃ as follows: ##EQU5## and at the same time, the parameters of theinverse matrix T₃₃ ⁻¹ are set to parameters b₁₁ to b₃₃ as follows:##EQU6## where, ##EQU7##

The equation (8) is substituted for the equation (6) to obtain thefollowing equation: ##EQU8##

Thereby, the following equation can be obtained: ##EQU9##

Here, the case where the positional vector [x_(m) y_(m) H₀ ] of thehomogeneous coordinates on the frame memory FM is transformed into thetwo-dimensional positional vector [X_(M) Y_(M) ] on the frame memory FMwill be described.

Since the parameter "H₀ " used when the two-dimensional positionalvector [X_(M) Y_(M) ] is transformed into the homogeneous coordinates isa parameter representing the size of the positional vector [x_(m) y_(m)] of the homogeneous coordinates, the parameters "x_(m) " and "y_(m) "representing the direction of the positional vector of the homogeneouscoordinates may be normalized with the parameter "H₀ " representing themagnification/reduction rate of the positional vector of homogeneouscoordinates, to transform the positional vector of the homogeneouscoordinates into the two-dimensional positional vector. Therefore,respective parameters "X_(s) " and "Y_(s) " of the two-dimensionalpositional vector on the monitor screen 55 are expressed by thefollowing equations: ##EQU10##

Similarly, in the case where the vector [x_(s) y_(s) 1] of homogeneouscoordinates on the monitor screen 55 is transformed into thetwo-dimensional positional vector [X_(S) Y_(S) ], the parameters "x_(s)" and "y_(s) " representing the direction of the positional vector ofhomogeneous coordinates may also be normalized with the parameter "1"representing the magnification/reduction rate of the positional vectorof homogeneous coordinates. Therefore, respective parameters "X_(S) "and "Y_(S) " of two-dimensional positional vector on the monitor screen55 are expressed by the following equations:

    X.sub.S =x.sub.s

    Y.sub.S =y.sub.s                                           (12)

Thus, the address (X_(M), Y_(M)) on the frame memory FM can be obtainedby the equation (10) as the following equation: ##EQU11##

Next, respective parameters of T₃₃ ⁻¹ will be obtained. ##EQU12## where,##EQU13##

Here, from the relation of the equation (7), the values of a₁₁ to a₃₃become as follow: ##EQU14##

These equations are substituted for the equations (15) to (24) to obtainthe following equations: ##EQU15## where, ##EQU16##

In this way, the values of the equations (28) to (37) are substitutedfor the equations (13) and (14), so that the read address (X_(M), Y_(M))supplied to the frame memory FM are given as follows: ##EQU17## where,"H₀ " is as follows: ##EQU18## Therefore, the read address (X_(M),Y_(M)) supplied to the frame memory FM can be expressed by usingrespective parameters (r₁₁ to r₃₃, l_(x), l_(y), l_(z), and s) of thethree-dimensional transformation matrix T₀ which are determined by thespatial image transforming device desired by an operator, and using theperspective value P_(Z) which is a parameter previously set.

Therefore, with respect to the equations (6) to (40), the screen address(X_(S), Y_(S)) is supplied for each pixel so as to correspond to theorder of raster scanning of the monitor screen 55, and the read address(X_(M), Y_(M)) on the frame memory FM corresponding to the suppliedscreen address can be calculated successively.

(4) Hexahedron in Virtual Space

In this embodiment, as shown in FIG. 8, a rectangular parallelepiped BOXin the three-dimensional virtual space on which the three-dimensionallytransformed source video signal is mapped exists with the position thatthe origin O of the three-dimensional coordinates is centered as astandard position.

The rectangular parallelepiped BOX has an object image displaying face(SideA) on which the three-dimensionally transformed source video signalV_(1A) is mapped (FIG. 3), a plane (SideA') facing to the object imagedisplaying face (SideA), a first side face (SideB) on which thethree-dimensionally transformed source video signal V_(1B) is mapped(FIG. 3), a plane (SideB') facing to the first side face, a second sideface (SideC) on which the three-dimensionally transformed source videosignal V_(1C) is mapped (FIG. 3) and the second side face (SideC).

In the rectangular parallelepiped BOX, the thickness between the objectimage displaying face (SideA) and the facing plane (SideA'), that is thethickness "h" for the object image displaying face (SideA) is set by anoperator. The object image displaying face (SideA) positioned at astandard position as shown in FIG. 8 is positioned at a place where itmoves for a distance h/2 in the minus direction of the z-axis from thexy-plane. The facing plane (SideA') of the object image displaying face(SideA) is positioned at a place where it moves for a distance h/2 inthe plus direction of the z-axis from the xy-plane.

In connection, the source video signals V_(1A), V_(1B), and V_(1C)before the three-dimensional transformation are respectively on thexy-plane on which the screen surface exists. By using the transformationmatrix M_(A) or M_(A) ' described later, the source video signal V_(1A)is mapped on the object image displaying face (SideA) of the rectangularparallelepiped BOX or the facing plane (SideA') by the standardposition, the source video signal V_(1B) is mapped on the first sideface (SideB) of the rectangular parallelepiped BOX which is positionedat the standard position or the facing plane (SideB'), and the sourcevideo signal V_(1C) is mapped on the second side face (SideC) of therectangular parallelepiped BOX which is positioned at the standardposition or the facing plane (SideC').

In this way, when the source video signals V_(1A), V_(1B), and V_(1C)are mapped on respective faces of the rectangular parallelepiped BOXplaced at the standard position, the rectangular parallelepiped BOXmoves from the standard position to an arbitrary position in thethree-dimensional space by the operation of operator, so that the videosignals mapped on respective faces of the rectangular parallelepiped BOXby the three-dimensional transformation matrix T₀ of which parametersare changed in accordance with the movement of the rectangularparallelepiped BOX, moves in accordance with the movement with keepingthe state of sticking on each face of the rectangular parallelepipedBOX.

(5) Mapping on Object Image Displaying Face (SideA)

In the image forming part 20 of FIG. 3, an operator operates to cut thedesired area of the source video signal V_(1A) input to the croppingcircuit 21. The source video signal V_(1A) is still a two-dimensionalimage placed on the xy-plane at the time when it is input to thecropping circuit 21. More specifically, in FIG. 9A that thethree-dimensional coordinates of xyz is viewed in the plus direction ofthe z-axis from the position of the view point PZ of the z-axis, whenthe cropping position of left end of the source video signal V_(1A) onthe xy-plane is represented by C_(AL), the cropping position of rightend is C_(AR), the cropping position of top end is C_(AT), and thecropping position of bottom end is C_(AB), the coordinates of fourapexes of the cropped source video signal V_(1A) are expressed asfollows: ##EQU19##

In connection, FIG. 9B shows the state where the three-dimensionalcoordinates of xyz is viewed from the plus direction of the y-axis tothe minus direction of the y-axis. The cropped source video signalV_(1A) exists from a coordinate "x₂ " of the x-axis over a coordinate"x₁ " on the xy-plane, and there is no cubic thickness in the z-axisdirection.

In this way, the source video signal V_(1A) cropped by the croppingcircuit 21 is stored in a frame memory FM₂₂ with the state where it isnot transformed.

The source video signal V_(1A) stored in the frame memory FM₂₂ isparallel displaced to the minus direction of the z-axis for a distanceh/2 by the movement matrix L_(A). The movement matrix L_(A) is a matrixfor making the z-axis coordinates of the source video signal V_(1A) tobe

-h/2, and is expressed by the following equation: ##EQU20##

Therefore, as shown in FIG. 10B in which the three-dimensionalcoordinates of xyz is viewed from the plus direction of the y-axis tothe minus direction of the y-axis, the source video signal V_(1A) placedon the xy-plane is parallel displaced for -h/2 to the minus direction ofthe z-axis by the movement matrix L_(A). As a result, the state isobtained that the source video signal V_(1A) moves to the position("-h/2" in the z-axis) where the object image displaying face (SideA) ofthe rectangular parallelepiped BOX (FIG. 8) to be mapped exists. In thisstate, the x-coordinates (x₂ to x₁) of the source video signal V_(1A) isnot changed.

In connection, FIG. 10A shows the state that the source video signalV_(1A) parallel displaced by the movement matrix L_(A) is viewed fromthe position of view point PZ on the z-axis. In this state, thecoordinates of each apex of the source video signal V_(1A) is notchanged.

The rate transformation and the skew transformation are performed byrate/skew transformation matrix T_(rs) on the source video signal V_(1A)thus parallel displaced. The rate transformation is a transformation fortwo-dimensionally magnifying/reducing the source video signal V_(1A),which is parallel displaced in the minus direction of the z-axis for adistance h/2 on the two-dimensional plane, with a desiredmagnification/reduction rate in the plus and minus direction of thex-axis and in the plus and minus direction of the y-axis with the centerof the source video signal V_(1A). In the rate transformation, when themagnification/reduction rate of the x-axis direction is set to "r_(x) ",the magnification/reduction rate of the y-axis is set to "r_(y) ", therate transformation matrix T_(rate) is expressed by the following:##EQU21##

The skew transformation is a transformation for two-dimensionallydistorting the source video signal V_(1A), which is parallel displacedin the minus direction of the z-axis for a distance h/2 on thetwo-dimensional plane, with a desired skew rate respectively in the plusand minus direction of the x-axis and in the plus and minus direction ofthe y-axis with the center of the source video signal V_(1A) as astandard. In the skew transformation, when the skew rate in the x-axisdirection is set to "s_(x) " and the skew rate in the y-axis directionis set to "s_(y) ", the skew transformation matrix T_(skew) is expressedby the following equation: ##EQU22##

Therefore, the rate/skew transformation matrix T_(rs) which is adecoding transformation matrix of the rate transformation and the skewtransformation is expressed by the following equation: ##EQU23##

In addition, when the coordinates of four points on the two-dimensionalplane which are transformed by the rate/skew transformation matrixT_(rs) are set to (x₁ ', y₁ '), (x₂ ', y₂ ') , (x₃ ', y₃ ') and (x₄ ',y₄ '), as shown in FIG. 11A, they are expressed by the followingequations: ##EQU24##

As described above, when a processing for mapping the first source videosignal V_(1A) on the object image displaying face (SideA) is arranged,the following equation is obtained from the equations (42) and (45)using M_(A) as a matrix for representing the mapping processing:

    M.sub.A =L.sub.A ·T.sub.rs                        (47)

Thereby, four points (x₁, y₁), (x₂, y₂), (x₃, y₃) , and (x₄, y₄) ontwo-dimensional plane of the source video signal V_(1A) shown in FIG. 9are mapped on four points (x₁ ', y₁ ', -h/2) , (x₂ ', y₂ ', -h/2), (x₃', y₃ ', -h/2) and (x₄ ', y₄ ', -h/2) of the object image displayingface (SideA) in the three-dimensional space shown in FIGS. 11A and 11Bby the matrix M_(A).

In connection, the transformation processing same as the above case ofmapping the source video signal V_(1A) on the object image displayingface (SideA) is performed also on the key signal K_(1A) input to theimage forming part 20 corresponding to the first source video signalV_(1A).

(6) Mapping on the Facing Plane (SideA') of Object Image Displaying Face(SideA)

In the image forming part 20 shown in FIG. 3, the source video signalV_(1A) input to the cropping circuit 21 is cut for a desired area by theoperation of operator. The source video signal V_(1A) is still atwo-dimensional image placed on the xy-plane at the time of inputting tothe cropping circuit 21. That is, in FIG. 9A that the three-dimensionalcoordinates of xyz is viewed in the plus direction of the z-axis fromthe position of view point PZ of the x-axis, when the cropping positionof left end of source video signal V_(1A) on the xy-plane is representedby "C_(AL) ", the cropping position of right end is "C_(AR) ", thecropping position of top end is "C_(AT) ", and the cropping position ofbottom end is "C_(AB) ", the coordinates of four apexes of the croppedsource video signal V_(1A) becomes the equation (41) described above.

The source video signal V_(1A) thus cropped at the cropping circuit 21is stored in the frame memory FM₂₂ (FIG. 3) in the state where it is nottransformed.

The source video signal V_(1A) stored in the frame memory FM₂₂ isparallel displaced for a distance h/2 in the plus direction of thez-axis by the movement matrix L_(A). The movement matrix L_(A) ' is amatrix for making the z-axis coordinates of source video signal V_(1A)to be +h/2, and is expressed by the following equation: ##EQU25##Therefore, the source video signal V_(1A) placed on xy-plane is paralleldisplaced for h/2 in the plus direction of the z-axis by the movementmatrix L_(A) '. As a result, the state is obtained that the source videosignal V_(1A) moves to the position (z-axis coordinate value is +h/2)where the facing plane (SideA') of the object image displaying face(SideA) of the rectangular parallelepiped BOX (FIG. 8) to be mappedexists. In this state, the x-coordinate (x₂ to x₁) of the source videosignal V_(1A) is not changed.

The rate transformation and the skew transformation are performed byrate/skew transformation matrix T_(rs) on the source video signal V_(1A)thus parallel displaced. The rate transformation is a transformation fortwo-dimensionally magnifying/reducing the source video signal V_(1A),which is parallel displaced in the plus direction of the z-axis for adistance h/2 on the two-dimensional plane, with a desiredmagnification/reduction rate respectively in the plus and minusdirection of the x-axis and in the plus and minus direction of they-axis with the center of the source video signal V_(1A) as a standard.The rate transformation T_(rate) is expressed by the same equation asthe above equation (43).

The skew transformation is a transformation for two-dimensionallydistorting the source video signal V_(1A), which is parallel displacedin the plus direction of the z-axis for a distance h/2 on thetwo-dimensional plane, with a desired skew rate respectively in the plusand minus direction of the x-axis and in the plus and minus direction ofthe y-axis with the center of the source video signal V_(1A) as astandard. The skew transformation matrix T_(skew) is expressed by thesame equation as the above equation (44).

Therefore, the rate/skew transformation matrix T_(rs) which is adecoding transformation matrix of the rate transformation and the skewtransformation is also expressed by the same equation as the aboveequation (45).

In addition, the coordinates of four points (x₁ ', y₁ '), (x₂ ', y₂ '),(x₃ ', y₃ ') , and (x₄ ', y₄ ') on the two-dimensional plane which aretransformed by the rate/skew transformation matrix T_(rs) are expressedby the same equations as the above equations (46).

As described above, when a processing for mapping the first source videosignal V_(1A) on the facing plane (SideA') of the object imagedisplaying face (SideA) is arranged, the following equation is obtainedusing M_(A) ' as a matrix for representing the mapping processing:

    M.sub.A '=L.sub.A '·T.sub.rs                      (49)

Thereby, four points (x₁, y₁), (x₂, y₂) , (x₃, y₃), and (x₄, y₄) ontwo-dimensional plane of the source video signal V_(1A) shown in FIG. 9are mapped on four points (x₁ ', y₁ ', -h/2), (x₂ ', y₂ ', -h/2), (x₃ ',y₃ ', -h/2), and (x₄ ', y₄ ', -h/2) of the facing plane (SideA') of theobject image displaying face (SideA) in three-dimensional space by thematrix M_(A) '.

In connection, the transformation processing same as the above case ofmapping the source video signal V_(1A) on the facing plane (Side') ofthe object image displaying face (SideA) is performed also on the keysignal K_(1A) input to the image forming part 20 corresponding to thefirst source video signal V_(1A).

(7) Mapping on First Side Face (SideB)

In the image forming part 30 of FIG. 3, an operator operates to cut thedesired area of the source video signal V_(1B) input to the croppingcircuit 31. The source video signal V_(1B) is still a two-dimensionalimage placed on the xy-plane at the time when it is input to thecropping circuit 31. More specifically, in FIG. 12A that thethree-dimensional coordinates of xyz is viewed in the plus direction ofthe z-axis from the position of the view point PZ of the z-axis, whenthe cropping position of left end of the source video signal V_(1B) onthe xy-plane is represented by C_(BL), the cropping position of rightend is C_(BR), the cropping position of top end is C_(BT), and thecropping position of bottom end is C_(BB), the coordinates of fourapexes of the cropped source video signal V_(1B) are expressed asfollows: (C_(BR), C_(BT)); (C_(BL), C_(BT)); (C_(BL), C_(BB)); and(C_(BR), C_(BB)).

In connection, FIG. 12B shows the state where the three-dimensionalcoordinates of xyz is viewed from the plus direction of the y-axis tothe minus direction of the y-axis. The cropped source video signalV_(1B) exists from "C_(BL) " over "C_(BR) " on the xy-plane, and thereis no cubic thickness in the z-axis direction.

In this way, the source video signal V_(1B) cropped at the croppingcircuit 31 is stored in a frame memory FM₃₂ (FIG. 3) with the statewhere it is not transformed.

The source video signal V_(1B) stored in the frame memory FM₃₂ after ithas been cropped by the cropping circuit 31 is parallel displaced by aparallel movement matrix L_(BO) so that the center of the cropped sourcevideo signal V_(1B) is positioned at the origin O of xy-plane. From thecoordinates position of four points C_(BL), C_(BR), C_(BT), and C_(BB)shown by cropping, the parallel movement matrix L_(BO) is expressed bythe following equation: ##EQU26##

Therefore, as shown in FIG. 13A in which the three-dimensionalcoordinates of xyz is viewed from the position of view point PZ on thez-axis, the source video signal V_(1B) is so moved by the parallelmovement matrix L_(BO) that the center of the source video signal V_(1B)overlaps with the origin O.

In connection, FIG. 13B shows the state that the three-dimensionalcoordinates of xyz is overlooked from the plus direction of the y-axisto the minus direction of the y-axis, and it can be found that thesource video signal V_(1B) moves on the xy-plane by the parallelmovement matrix L_(BO).

The magnification and reduction are performed by magnification/reductionmatrix S_(B) on the source video signal V_(1B) thus parallel displaced.The magnification or reduction is for magnifying or reducing the sourcevideo signal V_(1B) in the x-axis direction, so that the length in thex-direction of the cropped source video signal V_(1B) coincides with thelength of an edge H_(B) which comes in contact with the first side face(SideB) of the object image displaying face (SideA) described above inFIG. 8, and simultaneously for magnifying or reducing the source videosignal V_(1B) in the y-axis direction, so that the length in they-direction of the source video signal V_(1B) coincides with thethickness "h" of the rectangular parallelepiped BOX described above inFIG. 6.

In this magnification/reduction, when the magnification/reduction ratein the x-axis direction is set to r_(Bx), and themagnification/reduction rate in the y-axis direction is r_(By), thefollowing equations can be obtained: ##EQU27## using the length inx-axis direction of the cropped source video signal V_(1B), (C_(BR)-C_(BL)), and the length in the y-axis direction, (C_(BT) -C_(BB)).Therefore, when the magnification/reduction rate "r_(x) " in the x-axisdirection and the magnification/reduction rate "r_(y) " in the y-axisdirection of the rate transformation matrix T_(rate) described above inthe equation (43) are replaced to the magnification/reduction rates"r_(Bx) " and "r_(By) " expressed by the equation (51) respectively, themagnification/reduction transformation matrix S_(B) is represented bythe following equation: ##EQU28##

Therefore, as shown in FIG. 14A, the cropped source video signal V_(1B),which is placed at a position where the center overlaps with the originO, is magnified and reduced in the x-axis direction and y-axis directionby the magnification/reduction transformation matrix S_(B), with theorigin O being centered. At this time, as shown in FIG. 14B that thethree-dimensional coordinates of xyz is overlooked from the plusdirection of the y-axis to the minus direction, in the transformation ofthe source video signal V_(1B) by the magnification/reductiontransformation matrix S_(B), it can be found that the source videosignal V_(1B) is two-dimensionally transformed on the xy-plane.

In addition, in this embodiment, the magnification/reduction rate r_(Bx)and r_(By) which are matched to the edge H_(B) of the object imagedisplaying face (SideA) and the thickness "h" are obtained from the fourcropping values C_(BR), C_(BL), C_(BT), and C_(BB) specified byoperator. Thereby, as shown in FIG. 15A, the area of the source videosignal V_(1B) cropped by the four points (C_(BL), C_(BT)), (C_(BR),C_(BT)), (C_(BL), C_(BB)), and (C_(BR), C_(BB)) is magnified or reducedas a whole (this is referred to as "cropping priority").

On the contrary, the operator can directly crop the source vido signalV_(1B) with the desired magnification/reduction rate by inputting themagnification/reduction rate r_(Bx) and r_(By) and two cropping valuesC_(BR) and C_(BB). In this case, as shown in FIG. 15B, both ofmagnification/reduction rate are set to "1" to input two cropping valuesC_(BR) and C_(BT), so that the image in necessary area is cut as it isto obtain the necessary magnified/reduced image.

The source video signal V_(1B) thus magnified or reduced is rotated for90° around the x-axis by the rotational transformation matrix R_(Bx).the rotational transformation matrix R_(Bx) is a matrix for transformingthe source video signal V_(1B) on xy-plane onto xz-plane, and isexpressed by the following equation: ##EQU29##

Therefore, the magnified/reduced source video signal V_(1B) on thexy-plane described above in FIG. 14 is rotationally transformed on thexz-plane by the rotational transformation matrix R_(Bx), as shown inFIG. 16B that the three-dimensional coordinates of xyz is overlookedfrom the plus direction of the y-axis to the minus direction. As aresult, the first side face (SideB) of the rectangular parallelepipedBOX (FIG. 8) on which an image is mapped is positioned at an angle of90° for the object image displaying face (SideA), so that the sourcevideo signal (FIG. 16B) is rotationally displaced to a position of thesame angle (90°) for the object image displaying face (SideA).

In connection, FIG. 16A shows the state where the source video signalV_(1B) transformed on the xz-plane by the rotational transformationmatrix R_(Bx) is viewed from a position of view point PZ on the z-axis.In this state, the source video signal V_(1B) has no thicknes in they-axis direction.

The source video signal V_(1B) (FIG. 16) thus transformed on xz-plane isrotated by a predetermined angle θ_(B) around the z-axis by therotational transformation matrix R_(Bz). The rotational transformationmatrix R_(Bz) is a transformation matrix for inclining the source vidosignal V_(1B) (FIG. 16) on the xz-plane by a predetermined angle θ_(B)for the x-axis, and is expressed by the following equation: ##EQU30##

Therefore, the source video signal V_(1B) on the xz-plane describedabove in FIG. 16 is rotationally transformed at a position where the itis inclined by a predetermined angle θ_(B) for the x-axis with theorigin O being centered, as shown in FIG. 17A that the three-dimensionalcoordinates of xyz is viewed from the position of view point PZ on thez-axis. As a result, the source video signal V_(1A) to be mapped on theobject image displaying face (SideA) of the rectangular parallelepipedBOX (FIG. 8) is skew transformed as described above in FIG. 11, so thatthe source video signal (FIG. 17A) rotationally transformed by therotational transformation matrix R_(Bz) is rotationally displaced to aposition parallel to the first side face (SideB), with keeping an angleat 90° for the object image displaying face (SideA).

The parameter θ_(B) of the rotational transformation matrix R_(Bz) canbe obtained from the coordinate values of two points (x₁ ', y₁ '), (x₂', y₂ ') , or (x₄ ', y₄ ') , (x₃ ', y₃ ') of the first source videosignal V_(1A) skewed in FIG. 11, which can be represented by thefollowing

equation:

    θ.sub.B = tan .sup.-1 (-(y.sub.1 '-y.sub.2 '), (x.sub.1 '-x.sub.2 ')) (55)

In connection, FIG. 17B shows the state that the source video signalV_(1B) which is rotationally displaced by the rotational transformationmatrix R_(Bz) is viewed from the plus direction of the y-axis to theminus direction of the y-axis.

The source video signal V_(1B) (FIGS. 17A and 17B) rotationallytransformed so as to incline for a predetermined angle θ_(B) for thex-axis is parallel displaced along the xy-plane by the parallel movementmatrix L_(B). The parallel movement matrix L_(B) is a transformationmatrix for displacing the source video signal V_(1B) shown in FIGS. 17Aand 17B so as to overlap on the first side face (SideB) of therectangular parallelepiped BOX. In this case, the edge H_(B) of thefirst side face (SideB) of the object image displaying face (SideA) inFIGS. 17A and 17B is represented by a straight line connecting twopoints (x₁ ', y₁ ') and (x₂ ', y₂ '). Therefore, to map the source videosignal V_(1B) shown in FIGS. 17A and 17B on the first side face (SideB),it is needed that the source video signal V_(1B) is displaced so as tocoincide with the edge H_(B) by the parallel movement matrix L_(B).

The source video signal V_(1B) may be parallel displaced so that thecenter of the source video signal V_(1B) coincides with the middleposition of the two points (x₁ ', y₁ ') and (x₂ ', y₂ '). The parallelmovement matrix L_(B) is expressed by the following equation: ##EQU31##

Therefore, the source video signal V_(1B) described above in FIGS. 17Aand 17B is parallel displaced on the xy-plane by the parallel movementmatrix L_(B) so as to coincide with the edge H_(B), thereby mapped onthe first side face (SideB) of the rectangular parallelepiped BOX (FIG.8), as shown in FIG. 18A in which the three-dimensional coordinates ofxyz is viewed from the view point PZ.

In addition, FIG. 18B shows the state where the source video signalV_(1B) parallel displaced by the parallel movement matrix L_(B) isviewed from the plus direction of the y-axis to the minus direction ofthe y-axis.

As described above, when a processing of mapping the second source videosignal V_(1B) on the first side face (SideB) is arranged, with setting amatrix representing the mapping processing to "M_(B) ", the followingequation can be obtained:

    M.sub.B =L.sub.BO ·S.sub.B ·B.sub.Bx ·R.sub.Bz ·L.sub.B                                         (57)

Therefore, the source video signal V_(1B) on xy-plane shown in FIGS. 12Aand 12B is mapped on the first side face (SideB) of the rectangularparallelepiped BOX (FIG. 8).

In connection, the same transformation processing as the case describedabove of mapping the source video signal V_(1B) on the first side face(SideB) is performed also on the key signal K_(1B) input to the imageforming part 30 corresponding to the second source video signal V_(1B).

(8) Mapping on Facing Plane (SideB') of First Side Face (SideB)

In the image forming part 30 of FIG. 3, an operator operates to cut thedesired area of the source video signal V_(1B) input to the croppingcircuit 31. The source video signal V_(1B) is still a two-dimensionalimage placed on the xy-plane at the time when it is input to thecropping circuit 31. More specifically, in FIG. 12A that thethree-dimensional coordinates of xyz is viewed toward the plus directionof the z-axis from the position of the view point PZ of the z-axis, whenthe cropping position of left end of the source video signal V_(1B) onthe xy-plane is represented by "C_(BL) ", the cropping position of rightend is "C_(BR) ", the cropping position of top end is "C_(BT) ", and thecropping position of bottom end is "C_(BB) ", the coordinates of fourapexes of the cropped source video signal V_(1B) are expressed asfollows: (C_(BR), C_(BT)); (C_(BL), C_(BT)); (C_(BL), C_(BB)); and(C_(BR), C_(BB)).

The source video signal V_(1B) thus cropped at the cropping circuit 31is stored in a frame memory FM₃₂ (FIG. 3) with the state where it is nottransformed.

The source video signal V_(1B) stored in the frame memory FM₃₂ after ithas been cropped by the cropping circuit 31 is parallel displaced by aparallel movement matrix L_(BO) so that the center of the cropped sourcevideo signal V_(1B) is positioned at the origin O of xy-plane. Theparallel movement matrix L_(BO) has the same equation as the equation(50) described above. Therefore, as described in FIG. 13A, the sourcevideo signal V_(1B) is so moved by the parallel movement matrix L_(BO)that the center of the source video signal V_(1B) overlaps with theorigin O.

The magnification and reduction are performed by magnification/reductionmatrix S_(B) on the source video signal V_(1B) thus parallel displaced.The magnification/reduction transformation matrix S_(B) is the sameequation as the equation (52) described above.

Therefore, similar to the case shown in FIG. 14A, the cropped sourcevideo signal V_(1B), which is placed at a position where the centeroverlaps with the origin O, is magnified and reduced in the x-axisdirection and the y-axis direction by the magnification/reductiontransformation matrix S_(B), with the origin O being centered.

In addition, in mapping on the facing plane (SideB'), similar to thecase described in FIG. 15A, the magnification/reduction rate r_(Bx) andr_(By) which are suited for the edge H_(B) of the object imagedisplaying face (SideA) and the thickness "h" are obtained from the fourcropping values C_(BR), C_(BL), C_(BT), and C_(BB) specified byoperator. Thereby, the area of the source video signal V_(1B) cropped bythe four points (C_(BL), C_(BT)), (C_(BR), C_(BT)), (C_(BL), C_(BB)),and (C_(BR), C_(BB)) is magnified or reduced as a whole (this isreferred to as "cropping priority").

On the contrary, the operator can directly crop the source video signalV_(1B) with the desired magnification/reduction rate by inputting themagnification/reduction rate r_(Bx) and r_(By) and two cropping valuesC_(BR) and C_(BB). In this case, as described relating to FIG. 15B, bothof magnification/reduction rate are set to "1" to input two croppingvalues C_(BR) and C_(BT), so that the image in necessary area is cut asit is to obtain the necessary magnified/reduced image.

The source video signal V_(1B) thus magnified or reduced is rotated for90° around the x-axis by the rotational transformation matrix R_(Bx).The rotational transformation matrix R_(Bx) is the same equation as theequation (53). Therefore, the magnified/reduced source video signalV_(1B) on xy-plane is rotationally transformed onto xz-plane by therotational transformation matrix R_(Bx), as described in FIG. 16. As aresult, the facing plane (SideB') of the first side face (SideB) of therectangular parallelepiped BOX (FIG. 8) to be mapped is positioned at anangle of 90° for the object image displaying face (SideA), so that thesource video signal (FIG. 16(B)) is rotationally displaced to a positionof the same angle (90°) for the object image displaying face (SideA).

The source video signal V_(1B) (FIGS. 16A and 16B) thus transformed onthe xz-plane is rotated by a predetermined angle θ_(B) around the z-axisby the rotational transformation matrix P_(Bz). The rotationaltransformation matrix R_(Bz), is a transformation matrix for incliningthe source video signal V_(1B) (FIGS. 16A and 16B) on the xz-plane by apredetermined angle θ_(B) for the x-axis, and is expressed by the sameequation as the equation (54) described above. Therefore, the sourcevideo signal V_(1B) on the xz-plane described above in FIGS. 16A and 16Bis rotationally transformed to a position where the it is inclined for apredetermined angle θ_(B) from the x-axis with the origin O beingcentered, as described relating to FIGS. 17A and 17B. As a result, thesource video signal V_(1A) to be mapped on the object image displayingface (SideA) of the rectangular parallelepiped BOX (FIG. 8) isskew-transformed as described above in FIG. 11, so that the source videosignal (FIG. 17A) rotationally transformed by the rotationaltransformation matrix R_(Bz) is rotationally displaced to a positionparallel to facing plane (SideB') of the first side face (SideB), withkeeping an angle at 90° for the object image displaying face (SideA).

The parameter θ_(B) of the rotational transformation matrix R_(Bz) canbe obtained from the coordinate values of two points (x₁ ', y₁ ') and(x₂ ', y₂ ') , or (x₄ ', y₄ ') and (x₃ ', y₃ ') of the first sourcevideo signal V_(1A) skewed in FIGS. 11A and 11B, which can berepresented by the same equation as the equation (55).

The source video signal V_(1B) (FIGS. 17A and 17B) rotationallytransformed so as to incline by a predetermined angle θ_(B) for thex-axis is parallel displaced along the xy-plane by the parallel movementmatrix L_(B) '. The parallel movement matrix L_(B) is a transformationmatrix for displacing the source video signal V_(1B) shown in FIGS. 17Aand 17B so as to overlap on the facing plane (SideB') of the first sideface (SideB) of the rectangular parallelepiped BOX (FIG. 8). In thiscase, the edge H_(B) ' of the facing plane (SideB') facing to the edgeH_(B) ' of the first side face (SideB) of the object image displayingface (SideA) in FIGS. 17A and 17B is represented by a straight lineconnecting two points (x₄ ', y₄ ') and (x₃ ', y₃ ') . Therefore, to mapthe source video signal V_(1B) shown in FIGS. 17A and 17B on the facingplane (SideB') of the first side face (SideB), it is needed that thesource video signal V_(1B) is displaced so as to coincide with the edgeH_(B) ' by the parallel movement matrix L_(B) '.

Therefore, the source video signal V_(1B) may be parallel displaced sothat the center of the source video signal V_(1B) coincides with themiddle position of the two points (x₄ ', y₄ ') and (x₃ ', y₃ '). Theparallel movement matrix L_(B) ' is expressed by the following equation:##EQU32## Therefore, the source video signal V_(1B) described aboverelating to FIGS. 17A and 17B is parallel displaced on the xy-plane bythe parallel movement matrix L_(B) ' so as to coincide with the edgeH_(B) ', thereby it is mapped on the facing plane (SideB') of the firstside face (SideB) of the rectangular parallelepiped BOX (FIG. 8).

As described above, when a processing of mapping the second source videosignal V_(1B) on the facing plane (SideB') of the first side face(SideB) is arranged, with setting a matrix representing the mappingprocessing to "M_(B) '", the following equation can be obtained from theequations (50), (52), (53), (54), and (58):

    M.sub.B '=L.sub.BO ·S.sub.B ·R.sub.Bx ·R.sub.Bz ·L.sub.B '                                       (59)

Therefore, the source video signal V_(1B) on xy-plane shown in FIG. 12is mapped on the facing plane (SideB') of the first side face (SideB) ofthe rectangular parallelepiped BOX (FIG. 8).

In connection, the same transformation processing as the case describedabove of mapping the source video signal V_(1B) on the facing plane(SideB') of the first side face (SideB) is performed also on the keysignal K_(1B) input to the image forming part 30 corresponding to thesecond source video signal V_(1B).

(9) Mapping on Second Side Face (SideC)

In the image forming part 40 of FIG. 3, an operator operates to cut thedesired area of the source video signal V_(1C) input to the croppingcircuit 41. The source video signal V_(1C) is still a two-dimensionalimage placed on the xy-plane at the time when it is input to thecropping circuit 41. More specifically, in FIG. 19A that thethree-dimensional coordinates of xyz is viewed in the plus direction ofthe z-axis from the position of the view point PZ of the z-axis, whenthe cropping position of left end of the source video signal V_(1C) onthe xy-plane is represented by C_(CL), the cropping position of rightend is C_(CR), the cropping position of top end is C_(CT), and thecropping position of bottom end is C_(CB), the coordinates of fourapexes of the cropped source video signal V_(1C) are expressed asfollows: (C_(CR), C_(CT)); (C_(CL), C_(CT)); (C_(CL), C_(CB)); and(C_(CR), C_(CB))

In connection, FIG. 19B shows the state where the three-dimensionalcoordinates of xyz is viewed from the plus direction of the y-axis tothe minus direction of the y-axis. The cropped source video signalV_(1C) exists from "C_(1C) " over "C_(CR) " on the xy-plane, and thereis no cubic thickness in the z-axis direction.

The source video signal V_(1C) thus cropped at the cropping circuit 41is stored in a frame memory FM₄₂ (FIG. 3) with the state where it is nottransformed.

The source video signal V_(1C) stored in the frame memory FM₂ after ithas been cropped by the cropping circuit 41 is parallel displaced by aparallel movement matrix L_(CO) so that the center of the cropped sourcevideo signal V_(1C) is positioned at the origin O of xy-plane. From thecoordinates position of four points C_(CL), C_(CR), C_(CT), and C_(CB)specified by cropping, the parallel movement matrix L_(CO) is expressedby the following equation: ##EQU33##

Therefore, as shown in FIG. 20A in which the three-dimensionalcoordinates of xyz is viewed from the position of view point PZ on thez-axis, the source video signal V_(1C) is so moved by the parallelmovement matrix L_(CO) that the center of the source video signal V_(1C)overlaps with the origin O.

In connection, FIG. 20B shows the state that the three-dimensionalcoordinates of xyz is overlooked from the plus direction of the y-axisto the minus direction of the y-axis, and it can be seen that the sourcevideo signal V_(1C) moves on the xy-plane by the parallel movementmatrix L_(CO).

The magnification and reduction are performed by magnification/reductionmatrix S_(C) on the source video signal V_(1C) thus parallel displaced.The magnification or reduction is for magnifying or reducing the sourcevideo signal V_(1C) in the x-axis direction, so that the length in thex-direction of the cropped source video signal V_(1C) coincides with thelength of an edge H_(C) which comes in contact with the second side face(SideC) of the object image displaying face (SideA) described above inFIG. 8, and simultaneously for magnifying or reducing the source videosignal V_(1C) in the y-axis direction, so that the length in they-direction of the source video signal V_(1C) coincides with thethickness "h" of the rectangular parallelepiped BOX described above inFIG. 8.

In this magnification/reduction, when the magnification/reduction ratein the x-axis direction is set to r_(Cx), and themagnification/reduction rate in the y-axis direction is r_(Cy), thefollowing equations can be obtained: ##EQU34## using the length in thex-axis direction of the cropped source video signal V_(1C), (C_(CR)-C_(CL)), and the length in the y-axis direction, (C_(CT) -C_(CB)).Therefore, when the magnification/reduction rate "r_(x) " in the x-axisdirection and the magnification/reduction rate "r_(y) " in the y-axisdirection of the rate transformation matrix T_(rate) described above inthe equation (43) are replaced to the magnification/reduction rate"r_(Cx) " and the magnification/reduction rate "r_(Cy) " expressed bythe equation (61) respectively, the magnification/reductiontransformation matrix S_(C) is represented by the following equation:##EQU35##

Therefore, as shown in FIG. 21A, the cropped source video signal V_(1C),which is placed at a position where the center overlaps with the originO, is magnified and reduced in the x-axis direction and y-axis directionby the magnification/reduction transformation matrix S_(BC) with theorigin O being centered. At this time, as shown in FIG. 21B that thethree-dimensional coordinates of xyz is overlooked from the plusdirection of the y-axis to the minus direction, in the transformation ofthe source video signal V_(1C) by the magnification/reductiontransformation matrix S_(C), it can be found that the source videosignal V_(1C) is two-dimensionally transformed on the xy-plane.

In addition, in this embodiment, the magnification/reduction rate r_(Cx)and r_(Cy) which are suited for the edge H_(c) of the object imagedisplaying face (SideA) and the thickness "h" are obtained from the fourcropping values C_(CR), C_(CL), C_(CT), and C_(CB) specified byoperator. Thereby, as shown in FIG. 22A, the area of the source videosignal V_(1C) cropped by the four points (C_(CL), C_(CT)) , (C_(CR),C_(CT)) , (C_(CL), C_(CB)) , and (C_(CR), C_(CB)) is magnified orreduced as a whole (this is referred to as "cropping priority").

On the contrary, the operator can directly crop the source video signalV_(1C) with the desired magnification/reduction rate by inputting themagnification/reduction rate r_(Cx) and r_(Cy) and two cropping valuesC_(CR) and C_(CB). In this case, as shown in FIG. 22B, both ofmagnification/education rate are set to "1" to input two cropping valuesC_(CR) and C_(CT), so that the image in necessary area is cut as it isto obtain the necessary magnified/reduced image.

The source video signal V_(1C) thus magnified or reduced is rotated for90° around the x-axis by the rotational transformation matrix R_(Cx).The rotational transformation matrix R_(Cx) is a matrix for transformingthe source video signal V_(1C) on xy-plane onto xz-plane, and isexpressed by the following equation: ##EQU36## Therefore, themagnified/reduced source video signal V_(1C) on the xy-plane describedabove in FIGS. 21A and 21B is rotationally transformed on the xz-planeby the rotational transformation matrix R_(Cx), as shown in FIG. 23Bthat the three-dimensional coordinates of xyz is overlooked from theplus direction of the y-axis to the minus direction. As a result, thesecond side face (SideC) of the rectangular parallelepiped BOX (FIG. 8)to be mapped is positioned at an angle of 90° for the object imagedisplaying face (SideA), so that the source video signal (FIG. 23B) isrotationally displaced to a position of the same angle (90°) for theobject image displaying face (SideA).

In addition, FIG. 23A shows the state where the source video signalV_(1C) transformed on the xz-plane by the rotational transformationmatrix R_(Cx) is viewed from a position of view point PZ on the z-axis.In this state, the source video signal V_(1c) has no thickness in they-axis direction.

The source video signal V_(1C) (FIGS. 23A and 23B) thus transformed onxz-plane is rotated by a predetermined angle θ_(C) around the z-axis bythe rotational transformation matrix R_(Cz). The rotationaltransformation matrix R_(Cz) is a transformation matrix for incliningthe source video signal V_(1C) (FIGS. 23A and 23B) on the xz-plane by apredetermined angle θ_(c) for the x-axis, and is expressed by thefollowing equation: ##EQU37## Therefore, the source video signal V_(1C)on the xz-plane described above in FIG. 23 is rotationally transformedat a position where it is inclined for a predetermined angle θ_(c) fromthe x-axis with the origin O being centered, as shown in FIG. 24A thatthe three-dimensional coordinates of xyz is viewed from the position ofview point PZ on the z-axis. As a result, the source video signal V_(1A)to be mapped on the object image displaying face (SideA) of therectangular parallelepiped BOX (FIG. 8) is skew-transformed as describedabove in FIG. 11, thereby the source video signal (FIG. 24(A))rotationally transformed by the rotational transformation matrix R_(Cz)is rotationally displaced to a position parallel to the second side face(SideC), with keeping an angle at 90° for the object image displayingface (SideA).

The parameter θ_(c) of the rotational transformation matrix R_(Cz) canbe obtained from the coordinate values of two points (x₁ ', y₁ ') and(X₄ ', y₄ ') , or (x₂ ', y₂ ') and (x₃ ', y₃ ') of the first sourcevideo signal V_(1C) skewed in FIG. 11, which can be represented by thefollowing equation:

    θ.sub.c = tan .sup.-1 (-(y.sub.1 '-y.sub.4 '), (x.sub.1 '-x.sub.4 ')) (65)

In connection, FIG. 24B shows the state that the source video signalV_(1C) which is rotationally displaced by the rotational transformationmatrix R_(Cz) is viewed from the plus direction of the y-axis to theminus direction of the y-axis.

The source video signal V_(1C) (FIGS. 24A and 24B) rotationallytransformed so as to incline for a predetermined angle θ_(c) for thex-axis is parallel displaced along the xy-plane by the parallel movementmatrix L_(C). The parallel movement matrix L_(C) is a transformationmatrix for displacing the source video signal V_(1C) shown in FIGS. 24Aand 24B so as to overlap on the second side face (SideC) of therectangular parallelepiped BOX. In this case, the edge H_(C) of thesecond side face (SideC) of the object image displaying face (SideA) inFIGS. 24A and 24B is represented by a straight line connecting twopoints (x₁ ', y₁ ') and (x₄ ', y₄ '). Therefore, to map the source videosignal V_(1C) shown in FIG. 24 on the second side face (SideC), it isneeded that the source video signal V_(1C) is displaced so as tocoincide with the edge H_(C) by the parallel movement matrix L_(C).

The source video signal V_(1C) may be parallel displaced so that thecenter of the source video signal V_(1C) coincides with the middleposition of the two points (x₁ ', y₁ ') and (x₄ ', y₄ '). The parallelmovement matrix L_(C) is expressed by the following equation: ##EQU38##

Therefore, as shown in FIG. 25A that the three-dimensional coordinatesof xyz is viewed from the position of view point PZ on the z-axis, thesource video signal V_(1C) described above in FIGS. 24A and 24B isparallel displaced on the xy-plane by the parallel movement matrix L_(C)so as to coincide with the edge H_(C), thereby mapped on the second sideface (SideC) of the rectangular parallelepiped BOX (FIG. 8).

In addition, FIG. 25B shows the state where the source video signalV_(1C) parallel displaced by the parallel movement matrix L_(C) isviewed from the plus direction of the y-axis to the minus direction ofthe y-axis.

As described above, when a processing of mapping the second source videosignal V_(1C) on the second side face (SideC) is arranged, with settinga matrix representing the mapping processing to "M_(C) ", the followingequation can be obtained:

    M.sub.C =L.sub.CO ·S.sub.C ·R.sub.Cx ·R.sub.Cz ·L.sub.C                                         (67)

from the equations (60), (62), (63), (64), and (66). Therefore, thesource video signal V_(1C) on xy-plane shown in FIG. 19 is mapped on thesecond side face (SideC) of the rectangular parallelepiped BOX (FIG. 8).

In connection, the same transformation processing as the case describedabove of mapping the source video signal V_(1C) on the second side face(SideC) is performed also on the key signal K_(1C) input to the imageforming part 40, corresponding to the second source video signal V_(1C).

(10) Mapping on Facing Plane (SideC') of Second Side Face (SideC)

In the image forming part 40 of FIG. 3, an operator operates to cut thedesired area of the source video signal V_(1C) input to the croppingcircuit 41. The source video signal V_(1C) is still a two-dimensionalimage placed on the xy-plane at the time when it is input to thecropping circuit 41. More specifically, in FIG. 19A that thethree-dimensional coordinates of xyz is viewed in the plus direction ofthe z-axis from the position of the view point PZ of the z-axis, whenthe cropping position of left end of the source video signal V_(1C) onthe xy-plane is represented by C_(CL), the cropping position of rightend is C_(CR), the cropping position of top end is C_(CT), and thecropping position of bottom end is C_(CB), the coordinates of fourapexes of the cropped source video signal V_(1C) are expressed asfollows: (C_(CR), C_(CT)); (C_(CL), C_(CT)); (C_(CL), C_(CB)); and(C_(CR), C_(CB)).

The source video signal V_(1C) thus cropped at the cropping circuit 41is stored in a frame memory FM₄₂ (FIG. 3) with the state where it is nottransformed.

The source video signal V_(1C) stored in the frame memory FM₄₂ after ithas been cropped by the cropping circuit 41 is parallel displaced by aparallel movement matrix L_(CO) so that the center of the cropped sourcevideo signal V_(1C) is positioned at the origin O of xy-plane. Theparallel movement matrix L_(CO) is expressed by the same equation as theequation (60) describe above. Therefore, similar to the case describedabove relating to FIG. 20A, the source video signal V_(1C) is so movedby the parallel movement matrix L_(CO) that the center of the sourcevideo signal V_(1C) overlaps with the origin O.

The magnification and reduction are performed by magnification/reductionmatrix S_(C) on the source video signal V_(1C) thus parallel displaced.The magnification/reduction transformation matrix S_(C) is representedby the same equation as the equation (62) described above.

Therefore, similar to the case described above relating to FIG. 21A, thecropped source video signal V_(1C), which is placed at a position wherethe center overlaps with the origin O, is magnified and reduced in thex-axis direction and y-axis direction by the magnification/reductiontransformation matrix S_(BC) with the origin O being centered.

In addition, in mapping on the facing plane (SideC'), similar to thecase of FIG. 22A, the magnification/reduction rate r_(Cx) and r_(Cy)which are suited for the edge H_(C) of the object image displaying face(SideA) and the thickness "h" are also obtained from the four croppingvalues C_(CR), C_(CL), C_(CT), and C_(CB) specified by the operator.Thereby, the area of the source video signal V_(1C) cropped by the fourpoints (C_(CL), C_(CT)), (C_(CR), C_(CT)), (C_(CL), C_(CB)), and(C_(CR), C_(CB)) is magnified or reduced as a whole (this is referred toas "cropping priority").

On the contrary, the operator can directly crop the source video signalV_(1C) with the desired magnification/reduction rate by inputting themagnification/reduction rate r_(Cx) and r_(Cy) and two cropping valuesC_(CR) and C_(CB). In this case, as described relating to FIG. 22B, bothof magnification/reduction rate are set to "1" to input two croppingvalues C_(CR) and C_(CT), so that the image in necessary area is cut asit is to obtain the necessary magnified/reduced image.

The source video signal V_(1C) thus magnified or reduced is rotated for90° around the x-axis by the rotational transformation matrix R_(CX).The rotational transformation matrix R_(CX) is expressed by the sameequation as the equation (63). Therefore, the magnified/reduced sourcevideo signal V_(1C) on the xy-plane described above in FIG. 21 isrotationally transformed on the xz-plane by the rotationaltransformation matrix R_(CX) as described in FIGS. 23A and 23B. As aresult, the facing plane (SideC') of the second side face (SideC) of therectangular parallelepiped BOX (FIG. 8) to be mapped is positioned at anangle of 90° for the object image displaying face (SideA), so that thesource video signal (FIG. 23B) rotationally transformed by therotational transformation matrix R_(CX) is rotationally displaced to aposition of the same angle (90°) for the object image displaying face(SideA).

The source video signal V_(1C) (FIGS. 23A and 23B) thus transformed onxz-plane is rotated by a predetermined angle θ_(C) around the z-axis bythe rotational transformation matrix R_(CZ). The rotationaltransformation matrix R_(CZ) is a transformation matrix for incliningthe source video signal V_(1C) (FIGS. 23A and 23B) on the xz-plane by apredetermined angle θ_(C) for the x-axis, and is expressed by the sameequation as the equation (64). Therefore, the source video signal V_(1C)on the xz-plane described above in FIGS. 23A and 23B is rotationallytransformed at a position where it is inclined for a predetermined angleθ_(C) from the x-axis with the origin O being centered, as described inFIGS. 24A and 24B. As a result, the source video signal V_(1A) to bemapped on the object image displaying face (SideA) of the rectangularparallelepiped BOX (FIG. 8) is skew transformed as described above inFIG. 11, thereby the source video signal (FIG. 24A) rotationallytransformed by the rotational transformation matrix R_(CZ) isrotationally displaced to a position parallel to the facing plane(SideC') of the second side face (SideC), with keeping an angle at 90°for the object image displaying face (SideA).

The parameter θ_(C) of the rotational transformation matrix R_(CZ) canbe obtained from the coordinate values of two points (x₁ ', y₁ ') and(X₄ ', y₄ ') , or (x₂ ', y₂ ') and (x₃ ', y₃ ') of the first sourcevideo signal V_(1A) skewed in FIGS. 17A and 17B, which can berepresented by the same equation as the equation (65).

The source video signal V_(1C) (FIGS. 24A and 24B) rotationallytransformed so as to incline for a predetermined angle θ_(C) for thex-axis is parallel displaced along the xy-plane by the parallel movementmatrix Lag. The parallel movement matrix L_(C) ' is a transformationmatrix for displacing the source video signal V_(1C) shown in FIGS. 24Aand 24B so as to overlap on the facing plane (SideC') of the second sideface (SideC) of the rectangular parallelepiped BOX. In this case, theedge H_(C) ' of the facing plane (SideC') side facing to the edge H_(C)of the second side face (SideC) of the object image displaying face(SideA) in FIGS. 24A and 24B is represented by a straight lineconnecting two points (x₂ ', Y₂ ') and (X₃ ', Y₃ '). Therefore, to mapthe source video signal V_(1C) shown in FIG. 24 on the facing plane(SideC') of the second side face (SideC), it is needed that the sourcevideo signal V_(1C) is displaced so as to coincide with the edge H_(C) 'by the parallel movement matrix L_(C) '.

The source video signal V_(1C) may be parallel displaced so that thecenter of the source video signal V_(1C) coincides with the middleposition of the two points (x₂ ', y₂ ') and (X₃ ', y₃ '). The parallelexpressed by the following equation: ##EQU39## Therefore, the sourcevideo signal V_(1C) described above in FIG. 24 is parallel displaced onthe xy-plane by the parallel movement matrix L_(C) ' so as to coincidewith the edge H_(C) ', thereby mapped on the facing plane (SideC') ofthe second side face (SideC) of the rectangular parallelepiped BOX (FIG.8).

As described above, when a processing of mapping the second source videosignal V_(1C) on the facing plane (SideC') of the second side face(SideC) is arranged, with setting a matrix representing the mappingprocessing to M_(C) ', the following equation can be obtained:

    M.sub.C =L.sub.CO ·S.sub.C ·R.sub.CX ·R.sub.CZ ·L.sub.C '                                       (69)

from the equations (60), (62), (63), (64), and (66). Therefore, thesource video signal V_(1C) on xy-plane shown in FIG. 19 is mapped on thefacing plane (SideC') of the second side face (SideC) of the rectangularparallelepiped BOX (FIG. 8).

In connection, the same transformation processing as the case describedabove of mapping the source video signal V_(1C) on the facing plane(SideC') of the second side face (SideC) is performed also on the keysignal K_(1C) input to the image forming part 40 corresponding to thesecond source video signal V_(1C).

(11) Transformation processing of First Source Video Signal V_(1A)

The image forming part 20 of the image processing apparatus 10transforms the source video signal V_(1A) on a screen as if the image ofsource video signal V_(1A) were mapped on the object image displayingface (SideA) of the rectangular parallelepiped BOX moved to a desiredposition in the three-dimensional virtual space, by using the abovetransformation matrix T (Equation (3)) and the above matrix M_(A)(Equation (47)) for mapping the video signal on the object imagedisplaying face (SideA) of the rectangular parallelepiped BOX (FIG. 8)on the three-dimensional coordinates.

The procedure is shown in FIG. 26. The image processing apparatus 10uses a CPU 58 and a working memory (ROM 59, RAM 61) to firstly obtain atstep SP1 the matrix M_(A) for mapping the first source video signalV_(1A) on the object image displaying face (SideA) by using the movementmatrix L_(A) (Equation (42)) and the rate/skew transformation matrixT_(rs) (Equation (45)) as described relating to the equation (47). Asshown in FIG. 27, the source video signal V_(1A) on xy-plane is mapped(V_(1A-2)) by the matrix M_(A) on the object image displaying face(SideA) of the rectangular parallelepiped BOX at a standard position(the position where the center overlaps with the origin O) ofthree-dimensional coordinates of xyz.

When the matrix M_(A) is obtained at step SP1 of FIG. 26, the imageprocessing apparatus 10 proceeds to step SP2 to obtain thethree-dimensional transformation matrix T_(O) (Equation (1)) which is abasic step of the spatial image transformation for transforming thesource video signal V_(1A) on two-dimensional plane to a desiredposition of three-dimensional coordinates, and then proceeds to step SP3to obtain the perspective transformation matrix P_(O) (Equation (2))which is a basic step of the perspective transformation for, on thescreen, seeing through the source video signal V_(2A) moved onto thethree-dimensional space by the three-dimensional transformation matrixT_(O) obtained at step SP2.

Therefore, the video signal V_(1A-2) mapped on the object imagedisplaying face (SideA) of the rectangular parallelepiped BOX shown inFIG. 27 by the matrix M is displaced by the three-dimensionaltransformation matrix T_(O) onto the object image displaying face(SideA) of the rectangular parallelepiped BOX' moved to a desiredposition on the three-dimensional space (V_(2A)). Further, thethree-dimensionally transformed video signal V_(2A) is furtherperspective transformed on the screen of the xy-plane (perspectivetransformed video signal V_(3A)).

In this way, when the transformation matrix M_(A) for mapping the sourcevideo signal V_(1A) on the object image displaying face (SideA), and thebasic image transformation matrixes T_(O) and P_(O) for transforming thesource video signal V_(1A) at a desired position of three-dimensionalspace and for seeing through the source video signal V_(1A) on thescreen are obtained, the image processing apparatus 10 proceeds to stepSP4 to map the source video signal V_(1A) on the object image displayingface (SideA), thereafter, the transformation matrix T_(A) forperspective transforming it on the screen plane is obtained as follows:

    T.sub.A =M.sub.A ·T.sub.O ·P.sub.O       (70)

Here, as described in the equation (4), in the image processingapparatus 10, the source video signal V_(1A) stored in the frame memoryFM₂₂ and the perspective transformed video signal V_(3A) read from theframe memory FM₂₂ are both two-dimensional data, and the data in thez-axis direction in the three-dimensional space is substantially notused in the operation of read address. Therefore, in the transformationmatrix of the equation (70), a parameter in third line and third row foroperating the data in the z-axis direction is unnecessary for operatingthe read address for the frame memory FM₂₂.

Therefore, the matrix T_(A33) in which the parameter in third line andthird row is excluded from the transformation matrix T_(A) of theequation (70) is set as a transformation matrix having necessaryparameters in actual operation of two-dimensional read address.

In this way, when the transformation matrix T_(A33) of third line thirdrow is obtained, the image processing apparatus 10 proceeds to step SP5to obtain the matrix equation D_(A33) of the transformation matrixT_(A33), and proceeds to subsequent step SP6. The step SP6 is a step forjudging whether or not the value of the matrix equation D_(A33) of thetransformation matrix T_(A33) is plus.

Here, the relationship between the area S₁ of the source video signalV_(1A) and the area S₃ on a screen after the transformation by thetransformation matrix T_(A33) is expressed by the following equation:

    S.sub.3 =S.sub.1 det(T.sub.33)                             (71)

From the equation (71), when the value of the matrix equation D_(A33) ofthe transformation matrix T_(A33) is plus, the transformation of thesource video signal V_(1A) by the transformation matrix T_(A33) isvalid. More specifically, it shows a state that the video signalmovement transformed by the transformation matrix T_(A33) orients to itsoutside on the object image displaying face (SideA) of the rectangularparallelepiped BOX moved to a desired position in the three-dimensionalspace, that is, a state that the surface FRONT of the three-dimensionaltransformed video signal V_(2A) mapped on the object image displayingface (SideA) of the rectangular parallelepiped BOX orients to theoutside of the rectangular parallelepiped BOX'. At this time, the imageprocessing apparatus 10 obtains an affirmative result at step SP6, andproceeds to step SP7 to obtain parameters ball to b_(A33) from the aboveequations (28) to (36) for obtaining the read addresses X_(MA), Y_(MA)to the frame memory FM₂₂, based on the transformation matrix T_(A33)representing the transformation onto the object image displaying face(SideA).

Based on the parameters b_(A11) to b_(A33) thus obtained, the readaddresses X_(MA), Y_(MA) are obtained from the above equations (13) and(14), and the source video signal V_(1A) in the frame memory FM₂₂ isread by the read addresses X_(MA), Y_(MA), so that in FIG. 27, thesource video signal V_(1A) is mapped on the object image displaying face(SideA) of the rectangular parallelepiped BOX' moved to thethree-dimensional space, and simultaneously it can be perspectivetransformed on the screen surface of xy-plane. Therefore, theperspective transformed video signal V_(3A) is read from the framememory FM₂₂.

On the contrary, a negative result is obtained at step SP6 describedabove, this means that the value of matrix equation D_(A33) of thetransformation matrix T_(A33) is minus, and it can be found from theequation (71) that this state is not valid. More specifically, thisshows the state that the video signal movement-transformed by thetransformation matrix T_(A33) orients to the inside on the object imagedisplaying face (SideA) of the rectangular parallelepiped BOX' moved toa desired position in the three-dimensional space. That is, in FIG. 27,this shows the state that the surface FRONT of the three-dimensionaltransformed video signal V_(2A) mapped on the object image displayingface (SideA) of the rectangular parallelepiped BOX' orients to thedirection (inside direction of the rectangular parallelepiped BOX')opposite to the state of orienting outside the rectangularparallelepiped BOX.

More specifically, it can be found that this is not a state where theobject image displaying face (SideA) of the rectangular parallelepipedBOX' in the three-dimensional space is, as shown in FIG. 27, positionedat a view point PZ side from the facing plane (SideA') of the objectimage displaying face (SideA), but is a state where the facing plane(SideA') of the object image displaying face (SideA) is, as shown inFIG. 28, positioned at the view point PZ side. That is, in FIG. 27, therectangular parallelepiped BOX' in the three-dimensional space rotatesat 45° for the xy-plane. On the contrary, in FIG. 28, the rectangularparallelepiped BOX' in the three-dimensional space rotates at 225° forthe xy-plane.

In addition, in this state, the surface FRONT of the three-dimensionaltransformed video signal V_(2A) being the source video signal V_(3A)three-dimensionally transformed is mapped on the facing plane (SideA')so as to orient to inside the rectangular parallelepiped BOX', that isto the plus direction of the z-axis.

In this way, when a negative result is obtained at step SP6 in FIG. 26,the image processing apparatus 10 proceeds to step SP8 to obtain thematrix M_(A) ' for mapping the first source video signal V_(1A) on thefacing plane (SideA') of the object image displaying face (SideA) byusing the movement matrix L_(A) ' (Equation (48)) and the rate/skewtransformation matrix T_(rs) (Equation (45)), as described relating tothe equation (49). As shown in FIG. 26, the source video signal V_(1A)on the xy-plane is mapped on the facing plane (SideA') of the objectimage displaying face (SideA) of the rectangular parallelepiped BOX inthe three-dimensional coordinates of xyz by the matrix M' (V_(1A-2) ').

When the matrix M_(A) ' is obtained at step SP8 in FIG. 26, the imageprocessing apparatus 10 obtains the three-dimensional transformationmatrix T_(O) (Equation (1)) and the perspective transformation matrixP_(O) (Equation (2)) at steps SP9 and SP10, similar to the above stepsSP2 and SP3.

Therefore, the video signal V_(1A-2) ' mapped on the facing plane(SideA') of the object image displaying face (SideA) of the rectangularparallelepiped BOX in FIG. 28 is displaced (V_(2A) ') by thethree-dimensional transformation matrix T_(O) onto the facing plane(SideA') of the object image displaying face (SideA) of the rectangularparallelepiped BOX' moved to a desired position in the three-dimensionalspace. Further, the video signal V_(2A) ' three-dimensionally movementtransformed is perspective-transformed on the screen of xy-plane(perspective transformed video signal V_(3A) ').

In this way, when the transformation matrix M_(A) ' for mapping thesource video signal V_(1A) on the facing plane (SideA') of the objectimage displaying face (SideA), the basic image transformation matrixT_(O) for transforming to a desired position in the three-dimensionalspace, and the basic image transformation matrix P_(O) forperspective-transforming on the screen surface are obtained, the imageprocessing apparatus 10 proceeds to step SP11 to map the source videosignal V_(1A) on the facing plane (SideA') of the object imagedisplaying face (SideA) in the three-dimensional space, thereafter, thetransformation matrix T_(A) ' for perspective-transforming it on thescreen surface is obtained by the following equation:

    T.sub.A '=M.sub.A '·T.sub.O ·P.sub.O     (72)

Here, as described relating to the equation (4), in the image processingapparatus 10, the source video signal V_(1A) stored in the frame memoryFM₂₂ and the perspective transformed video signal V_(3A) read from theframe memory FM₂₂ are both two-dimensional data. In the operation of theread address, the data in the z-axis direction in the three-dimensionalspace is practically not used. Therefore, in the transformation matrixof the equation (72), the parameter in third line and third row foroperating the data in the z-axis direction is not needed to operationthe read address for the frame memory FM₂₂.

Therefore, the matrix T_(A33) in which the parameter in third line andthird row is removed from the transformation matrix T_(A) ' of theequation (72) is the transformation matrix having the parametersnecessary to operate the two-dimensional read address actually.

Thus, when the transformation matrix T_(A33) ' of three lines and threerows is obtained, the image processing apparatus 10 proceeds to stepSP12 to obtain the matrix equation D_(A33) ' of the transformationmatrix T_(A33) and proceeds to the following step SP13. Step SP13 is astep for judging whether or not the value of matrix equation D_(A33) 'is minus. When an affirmative result is obtained at step SP13, thisexpresses the state that the video signal movement displaced by thetransformation matrix T_(A33) ' orients to the inside at the facingplane (SideA') of the objective image displaying face (SideA) of therectangular parallelepiped BOX' moved to a desired position in thethree-dimensional space, that is, the state the surface FRONT of thethree-dimensionally transformed video signal V_(2A) ' mapped on thefacing plane (SideA') of the object image displaying face (SideA) of therectangular parallelepiped BOX' in FIG. 28 orients to the inside of therectangular parallelepiped BOX'. At this time, the image processingapparatus 10 proceeds to step SP14 to obtain the parameters b_(A11) tob_(A33) for obtaining the read addresses X_(MA), Y_(MA) to the framememory FM₂₂ based on the transformation matrix T_(A33) ' representingthe transformation to the facing plane (SideA') of the object imagedisplaying face (SideA), from the equations (28) to (36) describedabove.

On the basis of the thus obtained parameters b_(A11) to b_(A33), theread addresses X_(MA), Y_(MA) are obtained from the above equations (13)and (14) to read the source video signal V_(1A) in the frame memory FM₂₂by the read addresses X_(MA), Y_(MA). Thereby, the source video signalV_(1A) can be mapped on the facing plane (SideA') of the object imagedisplaying face (SideA) of the rectangular parallelepiped BOX' movedinto the three-dimensional space in FIG. 28, and it can be perspectivetransformed on the screen surface of xy-plane. Therefore, theperspective-transformed video signal V₃ ' is read from the frame memoryFM₂₂.

On the contrary, when a negative result is obtained at step SP13 in FIG.26, this shows that, for example in FIGS. 27 and 28, the rectangularparallelepiped BOX' in the three-dimensional space is rotated at anangle 90° for the xy-plane and both of the object image displaying face(SideA) and the facing plane (SideA') are not viewed from the view pointPZ. At this time, the image processing apparatus 10 dose not supply theparameters b_(A11) to b_(A3) from a CPU 58 to a read address generatingcircuit 25, and controls the perspective transformed video signal V_(3A)not to be read from the frame memory FM₂₂.

In this way, in accordance with the procedure of FIG. 26, the sourcevideo signal V_(1A) input to the image forming part 20 is mapped on theobject image displaying face (SideA) of the rectangular parallelepipedBOX' in the three-dimensional virtual space or on its facing plane(SideA'), and it is perspective transformed on the screen surface oftwo-dimensional plane as if the mapped image in the three-dimensionalspace exists in the three-dimensional space.

(12) Transformation processing of Second Source Video Signal V_(1B)

The image forming part 30 of the image processing apparatus 10transforms the source video signal V_(1B) on a screen as if the image ofsource video signal V_(1B) were mapped on the first side face (SideB) ofthe rectangular parallelepiped BOX moved to a desired position in thethree-dimensional virtual space, by using the above transformationmatrix T (Equation (3)) and the above matrix M_(B) (Equation (57)) formapping the source video signal on the first side face (SideB) of therectangular parallelepiped BOX (FIG. 8) in the three-dimensionalcoordinates.

The procedure is shown in FIG. 29. The image processing apparatus 10uses a CPU 58 and a working memory (ROM 59, RAM 61) to firstly obtain atstep SP21 the matrix M_(B) for mapping the first source video signalV_(1B) on the first side face (SideB) by using the parallel movementmatrix L_(BO) (Equation (50)), the magnification/reductiontransformation matrix S_(B) (Equation (52)), the rotationaltransformation matrix R_(BX) (Equation (53)), the transformation matrixR_(BZ) which inclines for a predetermined angle θ_(B). and the parallelmovement matrix L_(B) (Equation (56)) as described relating to theequation (57). As shown in FIG. 30, the source video signal V_(1B) onxy-plane is mapped (V_(1B-2)) by the matrix M_(B) on the first side face(SideB) of the rectangular parallelepiped BOX at a standard position(the position where the center overlaps with the origin O) ofthree-dimensional coordinates of xyz.

When the-matrix M is obtained at step SP21 of FIG. 29, the imageprocessing apparatus 10 proceeds to step SP22 to obtain thethree-dimensional transformation matrix T_(O) (Equation (1)) which is abasic step of the spatial image transformation for transforming thesource video signal V_(1B) on two-dimensional plane to a desiredposition of three-dimensional coordinates, and then proceeds to stepSP23 to obtain the perspective transformation matrix P_(O) (Equation(2)) which is a basic step of the perspective transformation for, on thescreen, seeing through the source video signal V_(2B) moved onto thethree-dimensional space by the three-dimensional transformation matrixT_(O) obtained at step SP22.

Therefore, the video signal V_(1B-2) mapped (V_(2B)) on the first sideface (SideB) of the rectangular parallelepiped BOX shown in FIG. 30 bythe matrix M is displaced by the three-dimensional transformation matrixT_(O) onto the first side face (SideB) of the rectangular parallelepipedBOX' moved to a desired position in the three-dimensional space.Further, the three-dimensionally transformed video signal V_(2B) isfurther perspective transformed on the screen of the xy-plane(perspective transformed video signal V_(3B)).

In this way, when the transformation matrix M_(B) for mapping the sourcevideo signal V_(1B) on the first side face (SideB), and the basic imagetransformation matrixes T_(O) and P_(O) for transforming the sourcevideo signal V_(1B) to a desired position of three-dimensional space andfor seeing through the source video signal V_(1B) on the screen planeare obtained, the image processing apparatus 10 proceeds to step SP24 tomap the source video signal V_(1B) on the first side face (SideB) in thethree-dimensional space, thereafter, the transformation matrix T_(B) forperspective transforming it on the screen plane is obtained as follows:

    T.sub.B =M.sub.B ·T.sub.O ·P.sub.O       (73)

Here, as described in the equation (4), in the image processingapparatus 10, the source video signal V_(1B) stored in the frame memoryFM₃₂ and the perspective transformed video signal V_(3B) read from theframe memory FM₃₂ are both two-dimensional data, and the data in thez-axis direction in the three-dimensional space is substantially notused in the operation of read address. Therefore, in the transformationmatrix of the equation (73), a parameter in third line and third row foroperating the data in the z-axis direction is unnecessary for operatingthe read address for the frame memory FM₃₂.

Therefore, the matrix T_(B33) in which the parameter in the third lineand third row is excluded from the transformation matrix T_(B) of theequation (73) is set as a transformation matrix having necessaryparameters in the actual operation of two-dimensional read address.

In this way, when the transformation matrix T_(B33) of three lines andthree rows is obtained, the image processing apparatus 10 proceeds tostep SP25 to obtain the matrix equation D_(B33) of the transformationmatrix T_(B33), and proceeds to subsequent step SP26. The step SP26 is astep for judging whether or not the value of the matrix equation D_(B33)of the transformation matrix T_(B33) is plus. When an affirmative resultis obtained at step SP26, similar to the case described at step SP6 ofFIG. 26, this shows the state that the video signal transformed to bedisplaced by the transformation matrix T_(B33) orients to the outside onthe first side face (SideB) of the rectangular parallelepiped BOX' movedto a desired position in the three-dimensional space, that is, the statethat the surface FRONT of the three-dimensional transformed video signalV_(2B) mapped on the first side face (SideB) of the rectangularparallelepiped BOX' in FIG. 28 orients to the outside of the rectangularparallelepiped BOX. At this time, the image processing apparatus 10proceeds to step SP27 to obtain parameters b_(B11) to b_(B33) from theabove equations (28) to (36) for obtaining the read addresses X_(MB),Y_(MB) for the frame memory FM₃₂, based on the transformation matrixT_(B33) representing the transformation onto the first side face(SideB).

Based on the parameters b_(B11) to b_(B33) thus obtained, the readaddress X_(MB), Y_(MB) is obtained from the above equations (13) and(14), and the source video signal V_(1B) in the frame memory FM₃₂ isread by the read address X_(MB), Y_(MB), so that in FIG. 28, the sourcevideo signal V_(1B) is mapped on the first side face (SideB) of therectangular parallelepiped BOX' moved into the three-dimensional space,and simultaneously it can be perspective-transformed on the screensurface of xy-plane. Therefore, the perspective-transformed video signalV_(3B) is read from the frame memory FM₃₂.

On the contrary, a negative result is obtained at step SP26 describedabove, similar to the case of step SP6 of FIG. 26, this shows the statethat the video signal transformed to be displaced by the transformationmatrix T_(B33) orients to the inside on the first side face (SideB) ofthe rectangular parallelepiped BOX' moved to a desired position in thethree-dimensional space. That is, in FIG. 30, this shows the state thatthe surface FRONT of the three-dimensional transformed video signalV_(2B) mapped on the first side face (SideB) of the rectangularparallelepiped BOX' orients to the direction opposite to the state oforienting outside the rectangular parallelepiped BOX' (inside directionof the rectangular parallelepiped BOX').

More specifically, it can be known that this is not a state where thefirst side face (SideB) of the rectangular parallelepiped BOX in thethree-dimensional space is, as shown in FIG. 30, positioned at a viewpoint PZ side from the facing plane (SideB') of the first side face(SideB), but is a state where the facing plane (SideB') of the firstside face (SideB) is, as shown in FIG. 31, positioned at the view pointPZ side. That is, in FIG. 30, the rectangular parallelepiped BOX in thethree-dimensional space rotates at 225° for the xy-plane. On thecontrary, in FIG. 31, the rectangular parallelepiped BOX' in thethree-dimensional space rotates at 45° for the xy-plane.

In addition, in this state, the surface FRONT of the three-dimensionaltransformed video signal V_(2B) ' being the source video signal V_(1B)three-dimensionally transformed is mapped on the facing plane (SideB')so as to orient to inside the rectangular parallelepiped BOX', that isto the plus direction of the z-axis.

In this way, when a negative result is obtained at step SP26 in FIG. 29,the image processing apparatus 10 proceeds to step SP28 to obtain thematrix M_(B) ' for mapping the second source video signal V_(1B) on thefacing plane (SideB') of the first side face (SideB) by using theparallel movement matrix L_(BO) (Equation (50)), themagnification/reduction transformation matrix S_(B) (Equation (52)), therotational transformation matrix R_(BX) (Equation (53)), and thetransformation matrix R_(BZ) for inclining for a predetermined angleθ_(B), and the parallel movement matrix L_(B) ' (Equation (58)), asdescribed relating to the equation (59). As shown in FIG. 31, the sourcevideo signal V_(1B) on xy-plane is mapped (V_(1B-2) ') on the facingplane (SideB') of the first side face (SideB) of the rectangularparallelepiped BOX in the three-dimensional coordinates of xyz by thematrix M_(B) '.

When the matrix M_(B) ' is obtained at step SP28 in FIG. 29, the imageprocessing apparatus 10 obtains the three-dimensional transformationmatrix T_(O) (Equation (1)) and the perspective transformation matrixP_(O) (Equation (2)) at steps SP29 and SP30, similar to the above stepsSP22 and SP23.

Therefore, the video signal V_(1B-2) ' mapped on the facing plane(SideB') of the first side face (SideB) of the rectangularparallelepiped BOX in FIG. 31 is displaced (V_(2B) ') by thethree-dimensional transformation matrix T_(O) to the facing plane(SideB') of the first side face (SideB) of the rectangularparallelepiped BOX moved to a desired position in the three-dimensionalspace. Further, the video signal V_(2B) ' three-dimensionallytransformed to be displaced is perspective-transformed on the screen ofxy-plane (perspective-transformed video signal V_(3B) ').

In this way, when the transformation matrix M_(B) ' for mapping thesource video signal V_(1B) on the facing plane (SideB') of the firstside face (SideB), the basic image transformation matrix T_(O) fortransforming to a desired position in the three-dimensional space, andthe basic image transformation matrix P_(O) for perspective-transformingon the screen surface are obtained, the image processing apparatus 10proceeds to step SP31 to map the source video signal V_(1B) on thefacing plane (SideB') of the first side face (SideB) in thethree-dimensional space, thereafter, the transformation matrix T_(B) 'for perspective-transforming it on the screen surface is obtained by thefollowing equation:

    T.sub.B '=M.sub.B '·T.sub.O ·P.sub.O     (74)

Here, as described relating to the equation (4), in the image processingapparatus 10, the source video signal V_(1B) stored in the frame memoryFM₃₂ and the perspective-transformed video signal V_(3B) read from theframe memory FM₃₂ are both two-dimensional data. In the operation of theread address, the data in the z-axis direction in the three-dimensionalspace is practically not used. Therefore, in the transformation matrixof the equation (74), the parameters in third line and third row foroperating the data in the z-axis direction is not needed to operate theread address for the frame memory FM₃₂.

Therefore, the matrix T_(B33) ' in which the parameters in third lineand third row is removed from the transformation matrix T_(B) ' of theequation (74) is the transformation matrix having the parametersnecessary to operate the two-dimensional read address actually.

Thus, when the transformation matrix T_(B33) ' of three lines and threerows is obtained, the image processing apparatus 10 proceeds to stepSP32 to obtain the matrix equation D_(B33) ' of the transformationmatrix T_(B33) ' and proceeds to the following step SP33. Step SP33 is astep for judging whether or not the value of matrix equation D_(B33) 'is minus. When an affirmative result is obtained at step SP33, thisexpresses the state that the video signal transformed to be displaced bythe transformation matrix T_(B33) ' orients to the inside on the facingplane (SideB') of the first side face (SideB) of the rectangularparallelepiped BOX' moved to a desired position in the three-dimensionalspace, that is, the state where the surface FRONT of thethree-dimensionally transformed video signal V_(2B) ' mapped on thefacing plane (SideB') of the first side face (SideB) of the rectangularparallelepiped BOX' in FIG. 31 orients to the inside of the rectangularparallelepiped BOX'. At this time, the image processing apparatus 10proceeds to step SP34 to obtain the parameters b_(B11) to b_(B33) forobtaining the read addresses X_(MB), Y_(MB) for the frame memory FM₃₂based on the transformation matrix T_(B33) ' representing thetransformation onto the facing plane (SideB') of the first side face(SideB), from the equations (28) to (36) described above.

On the basis of thus obtained parameters b_(B11) to b_(B33), the readaddress X_(MB), Y_(MB) are obtained from the above equations (13) and(14) to read the source video signal V_(1B) in the frame memory FM₃₂ bythe read address X_(MB), Y_(MB). Thereby, the source video signal V_(1B)can be mapped on the facing plane (SideB') of the first side face(SideB) of the rectangular parallelepiped BOX' moved into thethree-dimensional space in FIG. 31, and it can beperspective-transformed on the screen surface of xy-plane. Therefore,the perspective-transformed video signal V_(3B) ' is read from the framememory FM₃₂

On the contrary, when a negative result is obtained at step SP33 in FIG.29, this shows that, for example in FIGS. 30 and 31, the rectangularparallelepiped BOX in the three-dimensional space is not rotated for thexy-plane and both of the first side face (SideB) and the facing plane(Side') are not viewed from the view point PZ. At this time, the imageprocessing apparatus 10 dose not supply the parameters b_(B11) tob_(B33) from a CPU 58 to a read address generating circuit 35, andcontrols the perspective-transformed video signal V_(3B) not to be readfrom the frame memory FM₃₂.

In this way, in accordance with the procedure of FIG. 29, the sourcevideo signal V_(1B) input to the image forming part 30 is mapped on thefirst side face (SideB) of the rectangular parallelepiped BOX in thethree-dimensional virtual space or on its facing plane (SideB'), and itis perspective-transformed on the screen surface of two-dimensionalplane as if the mapped image in the three-dimensional space exists inthe three-dimensional space.

(13) Transformation processing of Third Source Video Signal V_(1C)

The image forming part 40 of the image processing apparatus 10transforms the source video signal V_(1C) on a screen as if the image ofsource video signal V_(1C) were mapped on the second side face (SideC)of the rectangular parallelepiped BOX moved to a desired position in thethree-dimensional virtual space, by using the above transformationmatrix T (Equation (3)) and the above matrix M_(C) (Equation (47)) formapping the source video signal on the second side face (SideC) of therectangular parallelepiped BOX (FIG. 8) on the three-dimensionalcoordinates.

The procedure is shown in FIG. 32. The image processing apparatus 10uses a CPU 58 and a working memory (ROM 59, RAM 61) to firstly obtain atstep SP41 the matrix M_(C) for mapping the third source video signalV_(1C) on the second side face (SideC) by using the parallel movementmatrix L_(CO) (Equation (60)), the magnification/reductiontransformation matrix S_(C) (Equation (62)), the rotationaltransformation matrix R_(CX) (Equation (63)), the transformation matrixR_(CZ) which inclines for a predetermined angle θ_(C), and the parallelmovement matrix L_(C) (Equation (66)) as described relating to theequation (67). The source video signal V_(1C) on xy-plane is mapped(V_(1C-2)) by the matrix M_(C) on the second side face (SideC) of therectangular parallelepiped BOX at a standard position (the positionwhere the center overlaps with the origin O) of three-dimensionalcoordinates of xyz.

When the matrix M_(C) is obtained at step SP41 of FIG. 32, the imageprocessing apparatus 10 proceeds to step SP42 to obtain thethree-dimensional transformation matrix T_(O) (Equation (1)) which is abasic step of the spatial image transformation for transforming thesource video signal V_(1C) on the two-dimensional plane to a desiredposition of the three-dimensional coordinates, and then proceeds to stepSP43 to obtain the perspective transformation matrix P_(O) (Equation(2)) which is a basic step of the perspective transformation for, on thescreen, seeing through the source video signal V_(2C) moved into thethree-dimensional space by the three-dimensional transformation matrixT_(O) obtained at step SP42.

Therefore, the video signal V_(1C-2) mapped on the second side face(SideC) of the rectangular parallelepiped BOX by the matrix M_(C) isdisplaced (V_(2C)) by the three-dimensional transformation matrix T_(O)onto the second side face (SideC) of the rectangular parallelepiped BOX'moved to a desired position in the three-dimensional space. Further, thethree-dimensionally transformed video signal V_(2C) is furtherperspective transformed on the screen plane of the xy-plane(perspective-transformed video signal V_(3C)).

In this way, when the transformation matrix M_(C) for mapping the sourcevideo signal V_(1C) on the second side face (SideC), and the basic imagetransformation matrixes T_(O) and P_(O) for transforming the sourcevideo signal V_(1C) to a desired position of the three-dimensional spaceand for seeing through the source video signal V_(1C) on the screen areobtained, the image processing apparatus 10 proceeds to step SP44 to mapthe source video signal V_(1C) on the second side face (SideC),thereafter, the transformation matrix T_(C) for perspective-transformingit on the screen is obtained as follows:

    T.sub.C =M.sub.C ·T.sub.O ·P.sub.O       (75)

Here, as described in the equation (4), in the image processingapparatus 10, the source video signal V_(1C) stored in the frame memoryFM₄₂ and the perspective-transformed video signal V_(3C) read from theframe memory FM₄₂ are both two-dimensional data, and the data in thez-axis direction in the three-dimensional space is substantially notused in the operation of read address. Therefore, in the transformationmatrix of the equation (75), parameters in third line and third row foroperating the data in the z-axis direction is unnecessary for operatingthe read address from the frame memory FM₄₂. Therefore, the matrixT_(C33) in which the parameter in third line and third row is excludedfrom the transformation matrix T_(C) of the equation (75) is set as atransformation matrix having necessary parameters in actual operation oftwo-dimensional read address.

In this way, when the transformation matrix T_(C33) of third line andthird row is obtained, the image processing apparatus 10 proceeds tostep SP45 to obtain the matrix equation D_(C33) of the transformationmatrix T_(C33), and proceeds to subsequent step SP46. The step SP46 is astep for judging whether or not the value of the matrix equation D_(C33)of the transformation matrix T_(C33) is plus. When an affirmative resultis obtained at step SP46, similar to the case described at step SP6 ofFIG. 26, this shows the state that the video signal transformed to bedisplaced by the transformation matrix T_(C33) orients to the outside onthe second side face (SideC) of the rectangular parallelepiped BOX'moved to a desired position in the three-dimensional space, that is, thestate that the surface FRONT of the three-dimensional transformed videosignal V_(2C) mapped on the second side face (SideC) of the rectangularparallelepiped BOX' orients to the outside of the rectangularparallelepiped BOX'. At this time, the image processing apparatus 10proceeds to step SP47 to obtain parameters b_(C11) to b_(C33) from theabove equations (28) to (36) for obtaining the read addresses X_(MC),Y_(MC) to the frame memory FM₄₂, based on the transformation matrixT_(C33) representing the transformation onto the second side face(SideC).

Based on the parameters b_(C11) to b_(C33) thus obtained, the readaddresses X_(MC), Y_(MC) are obtained from the above equations (13) and(14), and the source video signal V_(1C) in the frame memory FM₄₂ isread by the read addresses X_(MC), Y_(MC), so that the source videosignal V_(1C) is mapped on the second side face (SideC) of therectangular parallelepiped BOX' moved into the three-dimensional space,and simultaneously it can be perspective-transformed on the screensurface of xy-plane. Therefore, the perspective transformed video signalV_(3C) is read from the frame memory FM₄₂.

On the contrary, a negative result is obtained at step SP46 describedabove, similar to the case of step SP6 of FIG. 26, this shows the statethat the video signal transformed to be displaced by the transformationmatrix T_(C33) orients to the inside on the second side face (SideC) ofthe rectangular parallelepiped BOX' moved to a desired position in thethree-dimensional space. That is, this shows the state that the surfaceFRONT of the three-dimensional transformed video signal V_(2C) mapped onthe second side face (SideC) of the rectangular parallelepiped BOX'orients to the direction opposite to the state of orienting outside therectangular parallelepiped BOX' (inside direction of the rectangularparallelepiped BOX').

More specifically, it can be known that this is not a state where thesecond side face (SideC) of the rectangular parallelepiped BOX' in thethree-dimensional space is positioned at a view point PZ side from thefacing plane (SideC') of the second side face (SideC), but is a statewhere the facing plane (SideC') of the second side face (SideC) ispositioned at the view point PZ side.

In addition, in this state, the surface FRONT of the three-dimensionaltransformed video signal V_(2C) ' being the source video signal V_(1C)three-dimensionally transformed is mapped on the facing plane (SideC')so as to orient to inside the rectangular parallelepiped BOX', that isto the plus direction of the z-axis.

In this way, when a negative result is obtained at step SP46 in FIG. 32,the image processing apparatus 10 proceeds to step SP48 to obtain thematrix M_(C) ' for mapping the second source video signal V_(1C) on thefacing plane (SideC') of the second side face (SideC) by using theparallel movement matrix L_(CO) (Equation (60)), themagnification/reduction transformation matrix S_(C) (Equation (62)), therotational transformation matrix R_(CX) (Equation (63)), and thetransformation matrix R_(CZ) for inclining for a predetermined angleθ_(C), and the parallel movement matrix L_(C) ' (Equation (68)), asdescribed relating to the equation (69). The source video signal V_(1C)on xy-plane is mapped (V_(1C-2) ') on the facing plane (SideC') of thesecond side face (SideC) of the rectangular parallelepiped BOX in thethree-dimensional coordinates of xyz by the matrix M_(C) '.

When the matrix M_(B) ' is obtained at step SP48 in FIG. 32, the imageprocessing apparatus 10 obtains the three-dimensional transformationmatrix T_(O) (Equation (1)) and the perspective transformation matrixP_(O) (Equation (2)) at steps SP49 and SP50, similar to the above stepsSP42 and SP43.

Therefore, the video signal V_(1C-2) ' mapped on the facing plane(SideC') of the second side face (SideC) of the rectangularparallelepiped BOX is displaced (V_(2C) ') by the three-dimensionaltransformation matrix T_(O) to the facing plane (SideC') of the secondside face (SideC) of the rectangular parallelepiped BOX moved to adesired position in the three-dimensional space. The video signal V_(2C)' three-dimensionally transformed to be displaced is furtherperspective-transformed on the screen plane of xy-plane(perspective-transformed video signal V_(3C) ').

In this way, when the transformation matrix M_(C) ' for mapping thesource video signal V_(1C) on the facing plane (SideC') of the secondside face (SideC), the basic image transformation matrix T_(O) fortransforming to a desired position in the three-dimensional space, andthe basic image transformation matrix P_(O) for perspective-transformingon the screen surface are obtained, the image processing apparatus 10proceeds to step SP51 to map the source video signal V_(1C) on thefacing plane (SideC') of the second side face (SideC) in thethree-dimensional space, thereafter, the transformation matrix T_(C) 'for perspective-transforming it on the screen surface is obtained by thefollowing equation:

    T.sub.C '=M.sub.C '·T.sub.O ·P.sub.O     (76)

Here, as described relating to the equation (4), in the image processingapparatus 10, the source video signal V_(1C) stored in the frame memoryFM₄₂ and the perspective transformed video signal V_(3C) read from theframe memory FM₄₂ are both two-dimensional data. In the operation of theread address, the data in the z-axis direction in the three-dimensionalspace is practically not used. Therefore, in the transformation matrixof the equation (76), the parameters in the third line and third row foroperating the data in the z-axis direction are not needed to operate theread address for the frame memory FM₄₂.

Therefore, the matrix T_(C33) ' in which the parameters in the thirdline and third row is removed from the transformation matrix T_(B) ' ofthe equation (76) is the transformation matrix having the parametersnecessary to operate the two-dimensional read address actually.

Thus, the transformation matrix T_(C33) ' of three lines and three rowsis obtained, the image processing apparatus 10 proceeds to step SP52 toobtain the matrix equation D_(C33) ' of the transformation matrixT_(C33) ' and proceeds to the following step SP53. Step SP53 is a stepfor judging whether or not the value of matrix equation D_(C33) ' isminus. When an affirmative result is obtained at step SP53, thisexpresses the state that the video signal transformed to be displaced bythe transformation matrix T_(C33) ' orients to the inside on the facingplane (SideC') of the second side face (SideC) of the rectangularparallelepiped BOX' moved to a desired position in the three-dimensionalspace, that is, the state the surface FRONT of the three-dimensionallytransformed video signal V_(2C) ' mapped on the facing plane (SideC') ofthe second side face (SideC) of the rectangular parallelepiped BOX'orients to the inside of the rectangular parallelepiped BOX'. At thistime, the image processing apparatus 10 proceeds to step SP54 to obtainthe parameters b_(C11) to b_(C33) for obtaining the read addressesX_(MC), Y_(MC) for the frame memory FM₄₂ based on the transformationmatrix T_(C33) ' representing the transformation to the facing plane(SideC') of the second side face (SideC), from the equations (28) to(36) described above.

On the basis of thus obtained parameters b_(C11) to b_(C33) the readaddress X_(MC), Y_(MC) are obtained from the above equations (13) and(14) to read the source video signal V_(1C) in the frame memory FM₄₂ bythe read address X_(MC), Y_(MC). Thereby, the source video signal V_(1C)can be mapped on the facing plane (SideC') of the second side face(SideC) of the rectangular parallelepiped BOX moved into thethree-dimensional space, and it can be perspective-transformed on thescreen surface of xy-plane. Therefore, the perspective-transformed videosignal V_(3C) ' is read from the frame memory FM₄₂

On the contrary, when a negative result is obtained at step SP53 in FIG.32, this shows that, for example, the rectangular parallelepiped BOX' inthe three-dimensional space is not rotated for the xy-plane and both ofthe second side face (SideC) and the facing plane (SideC') are notviewed from the view point PZ. At this time, the image processingapparatus 10 dose not supply the parameters b_(C11) to b_(C33) from aCPU 58 to a read address generating circuit 35, and controls theperspective-transformed video signal V_(3C) not to be read from theframe memory FM₄₂.

In this way, in accordance with the procedure of FIG. 32, the sourcevideo signal V_(1C) input to the image forming part 30 is mapped on thesecond side face (SideC) of the rectangular parallelepiped BOX' in thethree-dimensional virtual space or on its facing plane (SideC'), and itis perspective-transformed on the screen surface of two-dimensionalplane as if the mapped image in the three-dimensional space exists inthe three-dimensional space.

(14) Operations and Effects of the Embodiment

With the above construction, firstly, an operator operates athree-dimensional pointing device or keys provided on a control panel56, to input parameters necessary for operating the read address used inthe image processing apparatus of this invention. Here, the parametersnecessary for operating the read address are respective croppingpositions of source video signals V_(1A), V_(1B), and V_(1C), thethickness for the object image displaying face (SideA) of therectangular parallelepiped BOX, the rate transformation rate in thex-axis direction r_(x), the rate transformation rate in the y-axisdirection r_(y), the skew rate in the x-axis direction s_(x), and theskew rate in the y-axis direction s_(y).

The CPU 58 of the image processing apparatus 10 receives theseparameters input from the control panel 56 and reflects these to theoperation of read address in real time. More specifically, the CPU 58monitors the change of parameters supplied from the control panel 56 foreach frame, and calculates the parameters b_(A11) to b_(A33), b_(B11) tob_(B33), b_(C11) to b_(C33) for calculating the read address based onthe supplied parameters for each frame.

Thereby, the parameters can be changed in real time for each frame inaccordance with the operator's operation, and the read address iscalculated in real time in accordance with the changed parameters.

Next, the operator operates the three-dimensional pointing device, etc.provided on the control panel 56 to instruct the three-dimensional imagetransformation to the source video signals V_(1A), V_(1B), and V_(1C).When the three-dimensional image transformation is instructed by theoperator, the CPU 58 receives the parameters "r₁₁ to r₃₃ ", "lx", "ly","lz" and "s" of the three-dimensional transformation matrix T_(O)specified by the operator from the control panel 56, and reflects theseparameters to the calculation of the read address in real time. Morespecifically, the CPU 58 monitors the change of the parameters for eachframe, and calculates the parameters b_(A11) to b_(A33), b_(B11) tob_(B33), and b_(C11) to b_(C33) for calculating the read address iscalculated based on the supplied parameters for each frame. Next, theCPU 58 calculates the parameters of three-dimensional transformationmatrix T₃₃ ⁻¹ based on the received parameters "r₁₁ to r₃₃ ", "lx","ly", "lz", and "s", so as to calculate the read addresses X_(MA),Y_(MA), X_(MB), Y_(MB), X_(MC), Y_(MC).

In this way, in the image processing apparatus 10, as shown in FIG. 8,as a size of the rectangular parallelepiped BOX which exists on thevirtual space of three-dimensional coordinates of xyz, the length ofedge H_(B) at a first side face (SideB) side of the object imagedisplaying face (SideA), the length of edge H_(B) ' at the facing plane(Side') of the first side face (SideB) side of the object imagedisplaying face (SideA), the length of edge H_(C) at a second side face(SideC) side of the object image displaying face (SideA), and the lengthof edge H_(C) ' at the facing plane (SideC') of the second side face(SideC) side of the object image displaying face (SideA) are specifiedbased on the points represented by xy-coordinates, (x₁, y₁), (x₂, y₂) ,(x₃, y₃) , and (x₄, y₄) .

Therefore, the source video signal V_(1B) mapped on the first side face(SideB) which contacts via the edge H_(B) to the object image displayingface (SideA) is transformed into that having a size to coincide to thelength of the edge H_(B) by the parameter r_(BX) of themagnification/reduction matrix S_(B). The source video signal V_(1B)mapped on the facing plane (SideB') of the first side face (SideB) whichcontacts via the edge H_(B) ' to the object image displaying face(SideA) is transformed into that having a size to coincide to the lengthof the edge H_(B) ' by the parameter r_(BX) of themagnification/reduction matrix S_(B). The source video signal V_(1C)mapped on the second side face (SideC) which contacts via the edge H_(C)to the object image displaying face (SideA) is transformed into thathaving a size to coincide to the length of the edge H_(C) by theparameter r_(CX) of the magnification/reduction matrix S_(C). The sourcevideo signal V_(1C) mapped on the facing plane (SideC') of the secondside face (SideC) which contacts via the edge H_(C) ' to the objectimage displaying face (SideA) is transformed into that having a size tocoincide to the length of the edge H_(C) ' by the parameter r_(CX) ofthe magnification/reduction matrix S_(C).

Further, as a size of the rectangular parallelepiped BOX, the thickness"h" between the object image displaying face (SideA) and the facingplane (SideA') is specified by an operator. Based on the thickness "h",the source video signal V_(1B) mapped on the first side face (SideB) istransformed into that having a size which coincides to the length of thethickness "h" by the parameter r_(BY) of the magnification/reductionmatrix S_(B). The source video signal V_(1B) mapped on the facing plane(SideB') of the first side face (SideB) is transformed into that havinga size which coincides to the length of the thickness "h" by theparameter r_(BY) of the magnification/reduction matrix S_(B). The sourcevideo signal V_(1C) mapped on the second side face (SideC) istransformed into that having a size which coincides to the length of thethickness "h" by the parameter r_(cy) of the magnification/reductionmatrix S_(C). The source video signal V_(1C) mapped on the facing plane(SideC') of the second side face (SideC) is transformed into that havinga size which coincides to the length of the thickness "h" by theparameter r_(cy) of the magnification/reduction matrix S_(C).

In this way, the source video signals V_(1B) and V_(1C) mapped onrespective planes of the rectangular parallelepiped BOX in thethree-dimensional space (first side face (SideB) and the facing plane(SideB'), and second side face (SideC) and the facing plane (SideC'))are transformed into that having a size in accordance with the size ofthe rectangular parallelepiped BOX. Further, by the movement matrixL_(B) and L_(B) ' and movement L_(C) and L_(C) ', the first side face(SideB) and the facing plane (SideB'), and the second side face (SideC)and the facing plane (SideC') are transformed so as to contact with theobject image displaying face (SideA).

Further, when the rectangular parallelepiped BOX in thethree-dimensional space is moved to a desired position by the operationof operator, in accordance with the change of respective parameters r₁₁to r₃₃, l_(x), l_(y), l_(z), the parameters b₁₁ to b₃₃ for generatingthe read addresses X_(M), Y_(M) from the frame memory FM are changed.Thereby, the respective source video signals V_(1A), V_(1B), and V_(1C)are moved in accordance with the movement of the rectangularparallelepiped BOX in the three-dimensional space, keeping the statewhere they stacks on the face to be mapped respectively.

Therefore, with the above constitution, the rectangular parallelepipedBOX in the three-dimensional space is only moved by the device ofoperator, and the respective source video signal V_(1A), V_(1B), andV_(1C) to be mapped on respective faces of the rectangularparallelepiped BOX are moved similarly in accordance with the movement,so that the respective source video signals V_(1A), V_(1B), and V_(1C)can be displayed on the screen surface 55A in real time by the simpleoperation of operator as if the rectangular parallelepiped BOX is movedin the three-dimensional space, keeping the state where the respectivesource video signals V_(1A), V_(1B), and V_(1C) are mapped on respectivefaces.

(15) Other Embodiments

Note that, the aforementioned embodiment has dealt with the case where,as described in FIG. 28, the perspective video signal V_(3A) ' mapped ona position of the facing plane (SideA') of the object image displayingface (SideA) and projected (seen through) on the xy-plane orients to theplus direction of the z-axis in FIG. 28. More specifically, the surfaceFRONT of the perspective video source V_(3A) ' orients not in thedirection of the view point PZ side, but in the opposite direction ofthe view point PZ. Therefore, the image that the perspective videosignal V_(3A) ' is viewed from its back is displayed on the screen, sothat the reverse image to the image to be displayed naturally isdisplayed.

Thereby, in this case, as shown in FIG. 33, the image processingapparatus 10 may has two reversal modes for making the source videosignal V₁ to be reversed so that the right side and the wrong side arereplaced, when the source video signal V₁ is stored in the frame memoryFM.

More specifically, the two reversal modes are a horizontal directionreversal mode and a vertical direction reversal mode described below.The horizontal reversal mode is, as shown in FIG. 33A, a method ofwriting the source video signal in the frame memory FM so that theimages of the left side and the right side for the y-axis are reversedin the horizontal direction. To realize this method, in a normal modefor writing the supplied source video signal V₁ which does not reversedin the frame memory FM as it is, when the write address for supplying itin the frame memory FM is (X_(W), Y_(W)), the code of the x-coordinatevalue of the write address is only replaced to reverse the image in thehorizontal direction (it is rotated for 180° with the y-axis beingcentered). Therefore, in the horizontal reversal mode, the write address(-X_(W), Y_(W)) is supplied in the frame memory FM, so as to reverse theright side and the wrong side of the image as shown in FIG. 33B. In FIG.33B, the reversed video signal V₁ orients to the direction of the backside of paper, and it can be read as a normal character when seen fromthe back of the paper.

On the contrary, the vertical direction reversal mode is, as shown inFIG. 34A, a mode of writing the source video signal V₁ in the framememory FM so that the entire images with the x-axis being centered inthe rotation are rotated for 180° (that is, the images of right and leftis reversed in the horizontal direction for the x-axis). That is, thecode of the y-coordinate value of the write address is only replaced toreverse the image in the vertical direction (it is rotated for 180° withx-axis being centered). Therefore, in the vertical reversal mode, thewrite address (x_(W), -Y_(W)) is supplied in the frame memory FM, so asto reverse the right side and the wrong side of the image as shown inFIG. 34B. In FIG. 34B, the reversed video signal orients to thedirection of the back side of paper, and it can be read as a normalcharacter when seen from the back of the paper.

The source video signal V_(1A) reversed as shown in FIGS. 33B and 34Band written in the frame memory FM orients to the plus direction ofz-axis as shown in FIG. 35. That is, the perspective video signal V_(3A)' which is mapped on the facing plane (SideA') of the object imagedisplaying face (SideA) and which is seen through on the xy-planeorients to the view point PZ as shown in FIG. 35. Therefore, the imagethat the perspective video signal v_(3A) ' is viewed from the front sideis displayed on the screen.

Further, the embodiment described above has dealt with the case wherethe rectangular parallelepiped BOX comprising six faces is used as asolid for moving the image in the three-dimensional space. However, thisinvention is not limited to this, but the other solid being variouspolyhedron can be also used.

Industrial Applicability

In the image amount apparatus for broadcasting, this invention can beutilized in the case of forming the special effect image.

We claim:
 1. A video processing apparatus, comprising:first video processing means for performing a spatial transformation on a first source video by reading said first source video from a first memory in accordance with a first read address data in order to generate a first two-dimensional transform video; second video processing means for performing a spatial transformation on a second source video by reading said second source video from a second memory in accordance with a second read address data in order to generate a second two-dimensional transform video; third video processing means for performing a spatial transformation on a third source video by reading said third source video from a third memory in accordance with a third read address data in order to generate a third two-dimensional transform video; composite means for combining said first, second and third two-dimensional transform video to generate a two-dimensional composite video; and control means for generating said first read address data, said second read address data and said third read address data, and for modifying said second read address data and said third read address data in accordance with said spatial transformation to be performed on said first source video so that said two-dimensional composite video image appears as a desired three-dimensional object.
 2. The video processing apparatus according to claim 1,wherein said spatial transformation is performed as a mapping transformation for mapping source video onto a predetermined face of said three-dimensional object, a three-dimensional transformation for transforming said source video mapped on said predetermined face of said three-dimensional object into three-dimensional space, and a perspective transformation for perspective-transforming said source video transformed in three dimensional space onto a screen surface.
 3. The video processing apparatus according to claim 2, whereinsaid mapping transformation includes a calculation algorithm including, a first mapping transformation matrix for mapping said first source video on a first face of said three dimensional object, a second mapping transformation matrix for mapping said second source video on a second face of said three dimensional object and third mapping transformation matrix for mapping said third source video on a third face of said three dimensional object, and wherein said three dimensional transforation is defined by a three dimensional transformation matrix, and said perspective transformation is defined by a perspective transformation matrix.
 4. The video processing apparatus according to claim 2, wherein:said first transformation matrix designated as M_(A), is expressed by the following equation:

    M.sub.A =L.sub.A ·T.sub.rs

where, L_(A) : a matrix for performing a linear displacement on said first source video, T_(rs) : a matrix for performing a rate/skew transformation on said first source video; said second transformation matrix, designated as M_(B), is expressed by the following equation:

    M.sub.B =L.sub.BO ·S.sub.B ·R.sub.BX ·R.sub.BZ ·L.sub.B

where, L_(BO) : a matrix for performing a linear displacement on said second source video based upon a crop operation, S_(B) : a matrix for performing a magnification/reduction of said second source video R_(BY) : a matrix for performing a rotation of the second source video around the y-axis R_(BZ) : a matrix for performing a rotation of the second source video around the Z-axis L_(B) : a matrix for performing a linear displacement on said second source video; said third transformation matrix M_(C) is expressed by the following equation:

    M.sub.C =L.sub.CO ·S.sub.C R.sub.CX ·R.sub.CZ ·L.sub.C

where, L_(CO) : a matrix for performing a linear displacement on said third source video based upon a crop operation, S_(C) : a matrix for performing magnification/reduction of said third source video, R_(CX) : a matrix for performing a rotation of the third source video around the X-axis, R_(CZ) : a matrix for performing a rotation of the third source video around the Z-axis, L_(C) : a matrix for performing a linear displacement on said third source video.
 5. The video processing apparatus according to claim 4 wherein:said three-dimensional transformation matrix T_(O) is expressed by the following equation: ##EQU40## where, r₁₁ to r₃₃ : parameters for transforming the source video for x-, y-, and z-axis of the three-dimensional coordinates of xyz l_(x) : a parameter for linearly displacing the source video in the x-axis direction; l_(y) : parameter for linearly displacing the source video in the y-axis direction; l_(z) : parameter for linearly displacing the source video in the z-axis direction; and s: a parameter for magnifying or reducing the scale of source video; and wherein said perspective transformation matrix P_(O) is expressed by the following equation: ##EQU41## where, P_(Z) : a perspective value.
 6. The video processing apparatus according to claim 5,wherein said control means does not use the z-axis element of said three-dimensional transformation matrix in the calculation of said read address data.
 7. The video processing apparatus according to claim 5, whereina calculation algorithm of said mapping transformation further includes a fourth mapping transformation matrix for mapping said first source video on an opposite face of said first face of said three-dimensional object, a fifth mapping transformation matrix for mapping said second source video on an opposite face of said second face of said three-dimensional object and sixth mapping transformation matrix for mapping said third source video on an opposite face of said third face of said three-dimensional object.
 8. The video processing apparatus according to claim 5, whereinsaid first source video to be transformed to said first two-dimensional transform video by the transformation matrix T_(A) is expressed by the equation:

    T.sub.A =M.sub.A T.sub.O P.sub.O

said second source video to be transformed to said second two-dimensional transform video.
 9. The video processing apparatus according to claim 8, wherein:a fourth mapping transformation matrix designated as M_(A) ' is expressed by the following equation:

    M.sub.A '=L.sub.A '·T.sub.rs

where, L_(A) ': a matrix for performing a linear displacement on said first source video, T_(rs) : a matrix for performing a rate/skew transformation on said first source video; a fifth mapping transformation matrix M_(B) ' designated as is expressed by the following equation:

    M.sub.B '=L.sub.BO ·S.sub.B ·R.sub.BX ·R.sub.BZ ·L.sub.B '

where, L_(BO) : a matrix for performing a linear displacement on said second source video based upon a crop operation, S_(B) : a matrix for performing a magnification/reduction of said second source video R_(BY) : a matrix for performing a rotation of the second source video around the y-axis, R_(BZ) : a matrix for performing a rotation of the second source video around the Z-axis, L_(B) ': a matrix for performing a linear displacement of said second source video; a sixth mapping transformation matrix M_(C) ' is expressed by the following equation:

    M.sub.C '=L.sub.CO ·S.sub.C ·R.sub.CX ·R.sub.CZ ·L.sub.C '

where, L_(CO) : a matrix for performing a linear displacement on said third source video based upon a crop operation, S_(C) : a matrix for performing a magnification/reduction of the third source video, R_(CX) : a matrix for performing a rotation of the third source video around the x-axis; R_(CZ) : a matrix for performing a rotation of the third source video around the z-axis, L_(C) ': a matrix for performing a linear displacement on said third source video.
 10. The video processing apparatus according to claim 1, further comprising:means for implementing a reduction rate priority mode for modifying the content of, said first source video, said second source video, and/or said third source video when said first source video, said second source video, and/or said third source video are transformed to said first, second and third transform video, respectively; and means for implementing a crop priority mode for reducing or magnifying the modified content of said first source video, said second source video, and/or said third source video into a size corresponding to a size of a respective face of said two-dimensional composite video image when said first source video, said second source video, and/or said third source video are transformed to said first, second or third transform videos, respectively.
 11. The video processing apparatus according to claim 5, whereinsaid first two-dimensional transform video written in a first memory, said second two-dimensional transform video written in a second memory, and said third two-dimensional transform video written in a third memory are each read out from each of said memories in accordance with an inverse matrix of said transformation matrix T_(O).
 12. The video processing apparatus according to claim 7, wherein said control means further comprises:face detect means for detecting which of said first face or said opposite face of the first face is to be viewed as visible before performing said spatial transformation on said first source video; and selecting means for selecting said first mapping transformation matrix or said fourth mapping transformation matrix based on the resultant of detection of said face detect means.
 13. A video processing method, comprising the steps of:performing a spatial transformation on a first source video by reading said first source video from a first memory in accordance with a first read address data in order to generate a first two-dimensional transform video; performing a spatial transformation on a second source video by reading said second source video from a second memory in accordance with a second read address data in order to generate a second two-dimensional transform video; performing a spatial transformation on a third source video by reading said third source video from a third memory in accordance with a third read address data in order to generate a third two-dimensional transform video; combining said first, second and third two-dimensional transform video to generate a two-dimensional composite video; generating said first read address data, said second read address data and said third read address data; and modifying said second read address data and said third read address data in accordance with said spatial transformation to be performed on said first source video so that said two-dimensional composite video image appears as a desired three-dimensional object.
 14. The video processing method according to claim 13, wherein said spatial transformation is performed as a mapping transformation for mapping source video onto a predetermined face of said three-dimensional object, a three-dimensional transformation for transforming said source video mapped on said predetermined face of said three-dimensional object into three-dimensional space, and a perspective transformation for perspective-transforming said source video transformed in three dimensional space onto a screen surface.
 15. The video processing method according to claim 14, whereinsaid mapping transformation includes a calculation algorithm including, a first mapping transformation matrix for mapping said first source video on a first face of said three dimensional object, a second mapping transformation matrix for mapping said second source video on a second face of said three dimensional object and third mapping transformation matrix for mapping said third source video on a third face of said three dimensional object, and wherein said three dimensional transforation is defined by a three dimensional transformation matrix, and said perspective transformation is defined by a perspective transformation matrix.
 16. The video processing method according to claim 14, wherein:said first transformation matrix designated as M_(A), is expressed by the following equation:

    M.sub.A =L.sub.A ·T.sub.rs

where, L_(A) : a matrix for performing a linear displacement on said first source video, T_(rs) : a matrix for performing a rate/skew transformation on said first source video; said second transformation matrix, designated as M_(B), is expressed by the following equation:

    M.sub.B =L.sub.BO ·S.sub.B ·R.sub.BX ·R.sub.BZ ·L.sub.B

where, L_(BO) : a matrix for performing a linear displacement on said second source video based upon a crop operation, S_(B) : a matrix for performing a magnification/reduction of said second source video R_(BY) : a matrix for performing a rotation of the second source video around the y-axis R_(BZ) : a matrix for performing a rotation of the second source video around the Z-axis L_(B) : a matrix for performing a linear displacement on said second source video; said third transformation matrix M_(C) is expressed by the following equation:

    M.sub.C =L.sub.CO ·S.sub.C ·R.sub.CX ·R.sub.CZ ·L.sub.C

where, L_(CO) : a matrix for performing a linear displacement on said third source video based upon a crop operation, S_(C) : a matrix for performing magnification/reduction of said third source video, R_(CX) : a matrix for performing a rotation of the third source video around the x-axis, R_(CZ) : a matrix for performing a rotation of the third source video around the Z-axis, L_(C) : a matrix for performing a linear displacement on said third source video.
 17. The video processing method according to claim 16, wherein:said three-dimensional transformation matrix is expressed by the following equation: ##EQU42## where, r₁₁ to r₃₃ : parameters for transforming the source video for x-, y-, and z-axis of the three-dimensional coordinates of xyz l_(x) : a parameter for linearly displacing the source video in the x-axis direction; l_(y) : a parameter for linearly displacing the source video in the y-axis direction; l_(z) : a parameter for linearly displacing the source video in the z-axis direction; and s: a parameter for magnifying or reducing the scale of source video; and wherein said perspective transformation matrix P_(O) is expressed by the following equation: ##EQU43## where, P_(Z) : a perspective value.
 18. The video processing method according to claim 17,wherein said control means does not use the z-axis element of said three-dimensional transformation matrix in the calculation of said read address data.
 19. The video processing method according to claim 17, whereina calculation algorithm of said mapping transformation further includes a fourth mapping transformation matrix for mapping said first source video on an opposite face of said first face of said three-dimensional object, a fifth mapping transformation matrix for mapping said second source video on an opposite face of said second face of said three-dimensional object and sixth mapping transformation matrix for mapping said third source video on an opposite face of said third face of said three-dimensional object.
 20. The video processing method according to claim 17, whereinsaid first source video to be transformed to said first two-dimensional transform video by the transformation matrix T_(A) is expressed by the equation:

    T.sub.A =M.sub.A ·T.sub.O ·P.sub.O

said second source video to be transformed to said second two-dimensional transform video by the transformation matrix T_(B) is expressed by the equation:

    T.sub.B =M.sub.B T.sub.O ·P.sub.O ;

and said third source video to be transformed to said third two-dimensional transform video by the transformation matrix T_(C) is expressed by the equation:

    T.sub.C =M.sub.C ·T.sub.O P.sub.O.


21. 21. The video processing method according to claim 20, wherein:a fourth mapping transformation matrix designated as M_(A) ' is expressed by the following equation:

    M.sub.A '=L.sub.A '·T.sub.rs

where, L_(A) ': a matrix for performing a linear displacement on said first source video, T_(rs) : a matrix for performing a rate/skew transformation on said first source video; a fifth mapping transformation matrix M_(B) ' designated as is expressed by the following equation:

    M.sub.B '=L.sub.BO ·S.sub.B ·R.sub.BX ·R.sub.BZ ·L.sub.B '

where, L_(BO) : a matrix for performing a linear displacement on said second source video based upon a crop operation, S_(B) : a matrix for performing a magnification/reduction of said second source video R_(BY) : a matrix for performing a rotation of the second source video around the y-axis, R_(BZ) : a matrix for performing a rotation of the second source video around the Z-axis, L_(B) ': a matrix for performing a linear displacement of said second source video; a sixth mapping transformation matrix M_(C) ' is expressed by the following equation:

    M.sub.C' =L.sub.CO ·S.sub.C ·R.sub.CX ·R.sub.CZ ·L.sub.C '

where, L_(CO) : a matrix for performing a linear displacement on said third source video based upon a crop operation, S_(C) : a matrix for performing a magnification/reduction of the third source video, R_(CX) : a matrix for performing a rotation of the third source video around the x-axis; R_(CZ) : a matrix for performing a rotation of the third source video around the z-axis, L_(C) ': a matrix for performing a linear displacement on said third source video.
 22. The video processing method according to claim 13, further comprising the steps of:implementing a reduction rate priority mode for modifying the content of, said first source video, said second source video, and/or said third source video when said first source video, said second source video, and/or said third source video are transformed to said first, second and third transform video, respectively; and implementing a crop priority mode for reducing or magnifying the modified content of said first source video, said second source video, and/or said third source video into a size corresponding to a size of a respective face of said two-dimensional composite video image when said first source video, said second source video, and/or said third source video are first source video transformed to said first, second or third transform videos, respectively.
 23. The video processing method according to claim 17, wherein said first two-dimensional transform video written in a first memory, said second two-dimensional transform video written in a second memory, and said third two-dimensional transform written in a third memory are each read out from each of said memories in accordance with an inverse matrix of said transformation matrix T_(O).
 24. The video processing method according to claim 19, further comprising the steps of:detecting which of said first face or said opposite face of said first face is to be viewed as visible before performing said spatial transformation on said first source video; and selecting said first mapping transformation matrix or said fourth mapping transformation matrix based on the resultant of detection.
 25. A video processing apparatus, comprising:first video processing means for performing a first image transformation on a first source image data in accordance with first transform parameters to generate a first two-dimensional transform video; second video processing means for performing a second image transformation on a second source image data in accordance with second transform parameters to generate a second two-dimensional transform video; third video processing means for performing a third image transformation on a third source image data in accordance with third transform parameters to generate a third two-dimensional transform video; composite means for combining said first, second and third two-dimensional transform video to generate a two-dimensional composite video; and control means for generating said first transform parameters, said second transform parameters and said third transform parameters, and for modifying said second transform parameters and said third transform parameters based on a modification in a first transform operation to be performed on said first source image data.
 26. A video processing method, comprising the steps of:performing a first image transformation on a first source image data in accordance with first transform parameters to generate a first two-dimensional transform video; performing a second image transformation on a second source image data in accordance with second transform parameters to generate a second two-dimensional transform video; performing a third image transformation on a third source image data in accordance with third transform parameters to generate a third two-dimensional transform video; combining said first, second and third two-dimensional transform video to generate a two-dimensional composite video; generating said first transform parameters, said second transform parameters and said third transform parameters; and modifying said second transform parameters and said third transform parameters based on a modification in a first transform operation to be performed on said first source image data. 